A pre-med student at UC-Berkeley in the early 1940s, Manza was drafted into the United States Army during World War II. He was serving as a medic in the Army when he was assigned to an acting troupe.

This part of his acting career continued to flourish through the 1960s, with appearances on such shows as 77 Sunset Strip, McHale's Navy, Perry Mason, Gomer Pyle, U.S.M.C. and Gunsmoke, continuing in the 1970s and 1980s on such series such as Get Smart, My Three Sons, Night Gallery, Police Woman, Hart to HartChico and the Man, Barney Miller, Benson, Simon and Simon, Night Court,Newhart and most notably Banacek, on which he co-starred as the perpetually puzzled chauffeur Jay Drury. He went on into the 1990s, with appearances on the long-running NBC-TV sitcom series Seinfeld, CBS-TV's The Nanny and NBC-TV's Friends. Manza also made appearances in several feature films, perhaps most memorably as the actor playing Hitler in Blazing Saddles ("They lose me after the bunker scene.") and as the Fisherman whose scene in the 1998 Godzilla was used as the film's first teaser. He maintained a very active career up until the time of his death.

Manza appeared on daytime television briefly in 1963 as an original cast member of the ABC-TV soap opera series General Hospital, where he played the role of Mike Costello. Manza went on to become a character actor appearing on many primetime TV series in guest role spots, beginning in the 1950s with the TV crime/drama series Highway Patrol, and Alfred Hitchcock Presents.

Manza died in January 2000 in Scripps Health-Encintas Hospital in Encinitas, California of a heart attack. He had also suffered a heart attack three weeks before his death; while filming a commercial for Budweiser.