Da Silva was a graduate of the Carnegie Institute of Technology, and learned the acting trade under the tutelage of Eva Le Gallienne, joining the Civic Repertory Theatre in 1928. He changed his surname to the Portuguese Da Silva, although Silverblatt had no family connection with Portugal or Brazil (the name is sometimes misspelled Howard De Silva).

Da Silva did summer stock at the Pine Brook Country Club, located in the countryside of Nichols, Connecticut, with the Group Theatre (New York) formed by Harold Clurman, Cheryl Crawford and Lee Strasberg in the 1930s and early 1940s.

Da Silva appeared in a number of Broadway musicals, including the role of Larry Foreman in the legendary first production of Marc Blitzstein's musical, The Cradle Will Rock (1938). Later, he costarred in the original 1943 stage production of Rodgers and Hammerstein's Oklahoma!, playing the role of the psychopathic Jud Fry. He was the easygoing Ben Marino who opposed Tammany Hall in the Pulitzer winning musical Fiorello!.

Da Silva appeared in over 60 motion pictures. Some of his memorable roles include a leading mutineer in The Sea Wolf (1941), playing Ray Milland's bartender in The Lost Weekend (1945), and the half-blind Criminal "Chicamaw 'One-Eye' Mobley" in They Live by Night (1949). He also released an album on Monitor Records (MP 595) of political songs and ballads entitled Politics and Poker.

Many of his early feature films were of the noir genre and he often played the nemesis in the plot, such as two early post-war roles: that of Eddie Harwood in The Blue Dahlia, and the sadistic Captain Francis Thompson in Two Years Before the Mast (both 1946). Da Silva's characterization of historic figures are among some of his most notable work: he was Lincoln's brawling friend Jack Armstrong in both play (1939) and film (1940) versions of Abe Lincoln in Illinois written by Robert Sherwood; Benjamin Franklin in the 1969–1972 stage musical 1776 and a reprisal of the role for the 1972 film version of the production; Soviet leader Nikita Khrushchev in The Missiles of October (1974); Franklin D. Roosevelt in The Private Files of J. Edgar Hoover (1977); and Louis B. Mayer in Mommie Dearest (1981).

Da Silva married Actress Marjorie Nelson in 1949. Da Silva and Nelson divorced in 1960.

Da Silva became one of hundreds of artists blacklisted in the entertainment industry during the House Committee on Unamerican Activities investigation into alleged Communist influence in the industry. Following his March 1951 testimony in which he repeatedly invoked his Fifth Amendment rights, his lead performance in the completed feature film Slaughter Trail was re-shot with actor Brian Donlevy. Da Silva continued to find work on the New York stage, but did not work in feature films again until 1961 when he appeared in his BAFTA nominated performance in David and Lisa. He was eventually cleared of any charges in 1960, but not before his career in television had also stalled, with no work between 1951 and 1959 when he appeared in The Play of the Week. The brief respite was followed by another television career void until his appearance in a 1963 episode of The Defenders. That was the beginning of the end of Da Silva's blacklist, and the show's Producer Herb Brodkin paired Da Silva with william Shatner when he created the television series For the People.

Da Silva returned to the stage. He was nominated for the 1960 Tony Award for Best Featured Actor in a Musical for his role as "Ben Marino" in Fiorello! (1959). After being blacklisted, Da Silva and Nelson left Los Angeles for New York to perform in The World of Sholom Aleichem.

Da Silva was nominated for the British BAFTA Film Award for Best Foreign Actor for his performance as Dr. Swinford in David and Lisa (1962). Da Silva portrayed Soviet Premier Khrushchev in the television docudrama The Missiles of October (1974). He won the Emmy Award for Outstanding Performance by a Supporting Actor in a Comedy or Drama Special for his role as Eddie in Verna: U.S.O. Girl (1978) with Sissy Spacek.

Da Silva's American television character work included the defense attorney representing the robot in The Outer Limits episode "I, Robot" (1964), and district attorney Anthony Cleese in For the People (1965). For his performance as Eddie in the Great Performances production of Verna: USO Girl (1978), the actor received a Primetime Emmy Award for Outstanding Performance by a Supporting Actor in a Comedy or Drama Special.

In 1969, Da Silva originated the role of Benjamin Franklin in the musical 1776. Four days before the show opened on Broadway, he suffered a minor heart attack but refused to seek medical assistance because he wanted to make sure critics saw his performance. After the four official critic performances were over, the cast left to go to the cast party and Da Silva went to the hospital and immediately took a leave of absence from the production. While Da Silva recuperated, his understudy, Rex Everhart, took over the role and performed on the cast recording. Da Silva was able to reprise his role in the 1972 film version and appeared on that Soundtrack album.

Specifically, he provided continuity announcements for episodes from season 12 through season 15, ostensibly to help North American audiences get acclimatized to the nature of serial storytelling, which was then uncommon on non-soap-operatic television in the United States and Canada. His narration accompanied the earliest runs of Doctor Who as broadcast on American PBS stations and Canadian broadcasters like TVOntario during the 1970s and early 1980s. Typically, after Doctor Who had been run on a station for a while, the linking narration was removed as unnecessary. Nevertheless, the announcements were so familiar a part of some viewers' experience of Doctor Who that they became a standard extra feature on BBC DVD releases of early Tom Baker serials.

He also did voice acting in 26 episodes of the popular 1974–82 radio thriller series CBS Radio Mystery Theater (between July 1974 and February 1977). In 1978, he recorded linking narration for episodes of the British television program Doctor Who broadcast in the United States.

Da Silva also played President Franklin D. Roosevelt in The Private Files of J. Edgar Hoover (1977), Hollywood mogul Louis B. Mayer in Mommie Dearest (1981), and American statesman Benjamin Franklin in 1776 (1972), as well as a documentary depicting the life of Ben Franklin shown at Franklin's house in Philadelphia. He appeared in two different film adaptations of F. Scott Fitzgerald's 1925 novel, The Great Gatsby. In the 1949 production with Alan Ladd as Gatsby, Da Silva played garage owner George Wilson; in the 1974 film with Robert Redford, Da Silva was Meyer Wolfsheim, the flamboyant gambler with the interesting cufflinks. In his final appearance on screen, Da Silva played a New York Photographer fascinated with the reclusive Greta Garbo in the film Garbo Talks (1984), directed by Sidney Lumet.