Page was born November 22, 1924 in Kirksville, Missouri, the second child of Edna Pearl (née Maize) and Leon Elwin Page who worked at Andrew Taylor Still College of Osteopathy and Surgery (combined with the American School of Osteopathy, eventually to form A.T. Still University). He was an author whose works included Practical Anatomy (1925), Osteopathic Fundamentals (1926), and The Old Doctor (1932). She had one older brother, Donald.

At age five, Page relocated with her family to Chicago, Illinois. Raised a Methodist, Page and her family were active parishioners the Englewood Methodist Church in Chicago, where she had her first foray into acting within the church's theatre group, playing Jo March in a 1941 production of Louisa May Alcott's Little Women. After graduating from Chicago's Englewood Technical Prep Academy, she attended the Goodman School of Drama at the Art Institute of Chicago (later renamed The Theatre School at DePaul University), with the intention of becoming a visual Artist or Pianist.

Page, a trained method actor, spent five years appearing in various repertory theater productions in the Midwest and in New York after graduating from college. On October 25, 1945, she made her New York stage debut in Seven Mirrors, a play devised by Immaculate Heart High School students from Los Angeles. The play ran for a total of 23 performances at Blackfriars Repertory Theatre on Manhattan's Upper East Side. In February 1952, Director José Quintero cast Page in a minor role in Yerma, a theatrical interpretation of a poem by Federico García Lorca, staged at Circle in the Square Theatre in New York City's Greenwich Village. Page was subsequently cast in the role of Alma in the Quintero-directed production of Summer and Smoke, written by Tennessee Williams (also staged at the Circle Theatre in 1952). Page's role in Summer and Smoke garnered her significant exposure, including a Drama Desk Award, and was profiled in Time magazine.

A native of Kirksville, Missouri, Page studied at the Art Institute of Chicago and with Uta Hagen and Lee Strasberg in New York City before being cast in her first credited part in the Western film Hondo (1953), which earned her her first Academy Award nomination for Best Supporting Actress. She was subsequently blacklisted in Hollywood based on her association with Hagen, and did not work in film for eight years. Page continued to appear in television and on stage, and earned her first Tony Award nomination for her performance in Sweet Bird of Youth (1959–60), a role she reprised in the 1961 film adaptation, the latter of which earned her a Golden Globe Award.

Her official film debut and role in Hondo, opposite John Wayne, garnering her a nomination for the Academy Award for Best Supporting Actress. Prior, she appeared in an uncredited role in Taxi. Speaking to a Kirksville newspaper, she said: "Actually Hondo wasn't my first movie. I had one small, but satisfactory scene in a Dan Dailey picture called Taxi, which was filmed in New York." Page was blacklisted in Hollywood after her debut in Hondo based on her association with Uta Hagen, and did not work in film for nearly ten years. Her work continued on Broadway playing a spinster in the 1954–1955 production of The Rainmaker, written by N. Richard Nash; and as the frustrated wife whose husband becomes romantically obsessed with a young Arab, played by James Dean, in the 1954 production of The Immoralist, written by Augustus Goetz and Ruth Goetz and based on the novel of the same name (1902) by André Gide. Page remained friends with Dean until his death the following year, and kept several personal mementos from the play—including two drawings by him—until her death. These items were later acquired by Heritage Auctions in 2006.

In 1959, Page earned an Emmy nomination, of Best Single Performance by an Actress, for her role in the Playhouse 90 episode "The Old Man," written by william Faulkner. She subsequently earned critical accolades for her performance in the 1959–1960 Broadway production of Tennessee Williams's Sweet Bird of Youth opposite Paul Newman, in which she originated the role of a larger-than-life, addicted, sexually voracious Hollywood legend trying to extinguish her fears about her career with a young hustler named Chance Wayne (played by Newman). For her performance, Page received her first nomination for the Tony Award for Best Actress in a Play, as well as the Sarah Siddons Award for her performance in Chicago. She and Newman subsequently starred in the 1962 film adaptation of the same name and Page earned a nomination for the Academy Award for Best Actress for the film.

Page was married to Violinist Alexander Schneider from 1954 to 1957. On September 8, 1963, she married actor Rip Torn, who was six years her junior, in Pinal, Arizona. Page bore him three children: a daughter, Actress Angelica Page, and twin sons, Anthony "Tony" and Jonathan "Jon" Torn, the latter of whom is a professor of communications at Northern Arizona University.

Page was trained as a method actor, and at times worked with psychoanalysts when developing her interpretations of roles. She once told the Los Angeles Times: "If I read a part and think I can connect to it, that I can touch people with it, I will do it, no matter what its size. And if I think I can't do something with a part, I won't take it." In a 1964 interview upon completing the Broadway run of The Three Sisters, Page discussed her method acting at length. When asked if she used emotional recall as a technique, she responded: "I would never shut it out. But I don't try to get one. My whole effort is to relax and keep the doors open so that there's room if one should pop up."

Between 1966 and 1969, Page appeared in two holiday-themed television productions based on stories by Truman Capote: "The Christmas Memory" (for ABC Stage 67) and the television film The Thanksgiving Visitor, both of which earned her two consecutive Emmy Awards for Best Actress. In 1967, Page appeared again onstage in Peter Shaffer's Black Comedy/White Lies, a production which also included Michael Crawford and Lynn Redgrave, who were making their Broadway debuts. The same year, she appeared opposite Fred MacMurray in the Walt Disney-produced musical The Happiest Millionaire. Bosley Crowther of The New York Times was critical of the film, noting: "Geraldine Page and Gladys Cooper...square off in one musical scene of socially up-staging each other that is drenched in perfumed vulgarity. But, then, the whole picture is vulgar. It is an over-decorated, over-fluffed, over-sentimentalized endeavor to pretend the lace-curtain millionaires are—or were—every bit as folksy as the old prize-fighters and the Irish brawlers in the saloon."

In 1969, Page starred opposite Ruth Gordon in the exploitation thriller What Ever Happened to Aunt Alice?, the third and final film in the Robert Aldrich-produced trilogy which followed What Ever Happened to Baby Jane? (1962) and Hush… Hush, Sweet Charlotte (1964). The film is based on the novel The Forbidden Garden by Ursula Curtiss and features Page as Claire Marrable, a recently widowed socialite, who, upon discovering that her husband has left her virtually nothing, hires a number of unsuspecting housekeepers whom she murders one by one and robs them of their life savings in order to keep up her extravagant lifestyle. Writing for The New York Times, Vincent Canby deemed the film "an amusingly baroque horror story told by a master misogynist," and praised Page's "affecting" performance.

Page subsequently appeared in the Don Siegel-directed thriller The Beguiled (1971) opposite Clint Eastwood, playing the headmistress of a Southern girls' boarding school who takes in a wounded Confederate soldier. Director Siegel called Page "certainly as fine an actor as I've ever worked with. I never have gotten along better with anyone than I did with her." This was followed by a supporting role in the comedy Pete 'n' Tillie (1972), for which she earned an Academy Award nomination for Best Supporting Actress. She also appeared in three episodes of Rod Serling's Night Gallery between 1972 and 1973. In January 1973, she returned to Broadway playing Mary Todd Lincoln opposite Maya Angelou in the two-character play Look Away, written by Jerome Kilty. Page received a nomination for the Tony Award for Best Featured Actress in a Play (her second Tony Award nomination) for the 1975 production of Alan Ayckbourn's Absurd Person Singular with Sandy Dennis and Richard Kiley.

She also had a supporting role as a charismatic Hollywood evangelist (modeled after Aimee Semple McPherson) in The Day of the Locust (1975), an adaptation of the Nathanael West novel of the same name. In 1977, she appeared as a nun in the British comedy Nasty Habits, and provided the voice role of Madame Medusa in the Walt Disney animated film The Rescuers. During this time, she also appeared on television, guest-starring in the popular series Kojak (1976) and Hawaii Five-O (1977).

In 1978, Page appeared as the mother of three siblings and wife of a prominent attorney in Woody Allen's Interiors. For her performance, Page was nominated for an Academy Award for Best Actress, and won a BAFTA Award for Best Actress in a Supporting Role. The New York Times's Vincent Canby lauded her performance in the film, writing: "Miss Page, looking a bit like a youthful Louise Nevelson with mink-lashed eyes, is marvelous — erratically kind, impossibly demanding, pathetic in her loneliness and desperate in her anger." The following year, in November 1979, Page was inducted into the American Theater Hall of Fame.

For her stage work on Broadway, Page earned a total of four Tony Award nominations, and was referred to by the New York Daily News as "one of the finest stage actors of her generation." She was inducted into the American Theatre Hall of Fame in 1979.

Beginning in the early 1980s, Page and Torn lived separately after he began dating Actress Amy Wright; Torn had first met Wright in 1976 and begun an affair shortly after. Page was aware of Torn and Wright's relationship, and appeared onstage opposite Wright in the 1977 Off-Broadway production of The Stronger, under Torn's direction. In 1983, Torn fathered a child with Wright. Upon the birth of the child, Page was questioned about her marriage by columnist Cindy Adams, to which she responded: "Of course Rip and I are still married. We've been married for years. We're staying married. What's the big fuss?" In spite of their separation, Page and Torn remained married until her death; her daughter described their relationship as still "close" up until Page died in 1987.

Also in 1983, Page invited the young Actress Sabra Jones Strasberg to her dressing room to talk to Sabra about how much she had liked her performance in St. Joan by Maxwell Anderson, in which Geraldine had just seen her play the part originated by Ingrid Bergman. During this conversation Sabra asked her advice in forming a classic theatre based on alternating repertory. This became the Mirror Theater Ltd with its repertory program the Mirror Repertory, and Page accepted the role of Founding Artist in Residence. Page remained continually active in theater, appearing in numerous repertory, Broadway, and Off-Broadway productions throughout the 1980s; this included roles in Inheritors (1983) by Susan Glaspell, Paradise Lost (1983) by Clifford Odets, Rain (1984) by John Colton (based on the short story "Miss Thompson" by W. Somerset Maugham), Vivat! Vivat Regina! by Robert Bolt (in which she played Elizabeth I), Clarence (1985) by Booth Tarkington, and The Madwoman of Chaillot (1985; in which she played the Madwoman to great acclaim).

Page earned her seventh Academy Award nomination for her performance in the dark comedy The Pope of Greenwich Village (1984). This marked a record at the time for most Academy Award nominations without a win, for which Page was tied with Peter O'Toole and Richard Burton (who themselves had also garnered seven nominations without winning). On television, Page had a supporting role in the miniseries The Dollmaker (1984), opposite Jane Fonda and Amanda Plummer. In 1985, she apepared in the British horror film The Bride opposite Sting and Jennifer Beals; the drama White Nights, directed by Taylor Hackford; and opposite Rebecca de Mornay in the drama The Trip to Bountiful, in which she played an aging Southern Texas woman seeking to return to her hometown. The role earned Page wide critical acclaim, with the Los Angeles Times referring to it as "the performance of a lifetime."

Page earned a total of seven Academy Award nominations before winning her first Academy Award for Best Actress in 1985 for The Trip to Bountiful. She was also a winner of two Golden Globe Awards, two Primetime Emmy Awards, and one BAFTA award.

During her life, Page was regarded as a respected character Actress. Speaking of her stage career in 1986, she said: "I used to think that by opening [night] all the work was done. Now I'm finding how much you can learn from the audience." She described acting as a "bottomless cup," adding: "If I studied for the next ninety years I'd just be scratching the surface."

On June 13, 1987, Page failed to arrive at the Neil Simon Theatre for both the afternoon and evening performances of Sir Noël Coward's Blithe Spirit, which had begun its run in March. At the end of the show's evening performance, the play's Producer announced that Page had been found dead in her lower Manhattan townhouse. She was determined to have died of a heart attack.

She was also portrayed by her daughter, Angelica Page, in the stage production Turning Page. A monologue play chronicling Page's life, it was also written by her daughter: "I grew up in the center of her sparkling career," Angelica recalled. "As her only daughter I feel compelled to share her lessons and gifts with others who did and did not have the opportunity to know her magic intimately. She was a true rebel and trail blazer. A masterful woman who was ahead of her time and should not be forgotten anytime soon." The play premiered in Los Angeles in 2016, followed by performances in New York City in 2017.

Page was portrayed by Sarah Paulson in the 2017 anthology television series Feud, which chronicles the rivalry between actresses Bette Davis and Joan Crawford on the set of What Ever Happened to Baby Jane? (1962).