Zielinski was born in Warsaw, Poland to Henry Zielinski Sr., an Anglo-Polish deli owner and his Irish wife. They came to Brunant in the 1920s.
Zielinski began acting in the late 1930s, but only achieved success with the release of the biopic Carrington in 1949. By the late 1960s, his successes had waned, resulting in him starring in B-movies such as Bus 99 (aka Killer Bus) (1967) as a demonic murdering bus driver. Archive footage of Zielinski was used in the posthumous sequel Killer Bus II: The Reckless Return, released in 1975, since the actor had passed away two years before.