Born in Dawson, Texas, to Rufus Franklin and Nola (née Dell) Comer, her first major television credit was a guest appearance in a 1963 episode of Gunsmoke, followed by roles in several other dramatic series of the 1960s, such as Dr. Kildare and Bonanza. In 1964, she earned an Emmy nomination for Outstanding Performance in a Supporting Role by an Actress for her work on an episode on Arrest and Trial.

She made her feature film debut as the female lead in the 1964 comedy Quick, Before It Melts followed by a memorable role in the 1965 satire The Loved One, playing a seductive mortician who offers Robert Morse a choice for his uncle's funeral arrangements of "Inhumement, entombment, inurnment, immurement? Some people just lately have preferred ensarcophagusment."

Although Comer was cast opposite Michael Caine for Funeral In Berlin and even appeared in publicity stills, she had to be replaced because of illness. She had another leading role as a love interest to Marlon Brando and John Saxon in the Western adventure The Appaloosa (1966). The film, shot on location in Mexico, presented Anjanette as a Mexican peasant girl, a role she repeated in Guns for San Sebastian (1968). In between she starred in Banning.

Comer's movie activity dropped off in 1970 after she played Ruth in the film version of John Updike's Rabbit, Run (1970). She later claimed she let her love life interfere with her work. Comer's later films include Fire Sale (1977) and the made-for-TV The Long Summer of George Adams (1983). In subsequent years, she was frequently cast as mysterious or exotic characters.

From 1976 to 1983, she was married to Robert Klane; they later divorced.