Longer lasting was a later teaming with Avery Schreiber, whom he met when they were both members of The Second City, a live comedy and improv club based in Chicago. Burns and Schreiber were best known for a series of routines in which Burns played a talkative taxicab passenger, with Schreiber as the driver.
Burns played the dedicated but inept deputy sheriff Warren Ferguson during the first half of the 1965-1966 season of The Andy Griffith Show, as Barney Fife's replacement after Don Knotts left the cast. His character was not popular and was dropped without explanation after eleven appearances. The series did not have a deputy after Burns left the cast, though Goober Pyle was available in an emergency.
Burns voiced the character Ralph Kane in the syndicated cartoon Wait Till Your Father Gets Home (1972-1974).
Burns was the head writer for the first season of The Muppet Show. His comedy partner Avery Schreiber appeared on an episode of the first season. He also co-wrote The Muppet Movie (with Jerry Juhl, his successor as head writer of The Muppet Show).
Jack Burns hosted a 1977 episode of Saturday Night Live, which became the first episode where the show changed its name from "NBC's Saturday Night" to "Saturday Night Live" after Saturday Night Live with Howard Cosell was canceled.
In the early 1980s, Burns became a writer and sometimes-performer for the ABC sketch show Fridays (which was modeled heavily after SNL.) He and comedian Michael Richards were involved in a staged on-air fight with Andy Kaufman, later re-created in the Kaufman biopic Man on the Moon.
He was teamed with Lorenzo Music to provide the voices for a pair of crash test dummies in a series of public service announcements on car safety. In 1993, Burns starred in the cartoon-series Animaniacs, as the voice of Sid the Squid, giving the character a raspy, Daffy Duck kind of voice. Former partner Avery Schreiber also appeared on the show as Beanie the Bison.