Gautier started his career as a night-club comic and a singer for dance orchestras; he joined ASCAP in 1959 after serving in the United States Navy. In 1960, he portrayed fictional rock 'n roll star Conrad Birdie in the original Broadway theatre production of Bye Bye Birdie, receiving a Tony Award nomination for his performance. He was married to actress Barbara Stuart.
During the '70s and '80s, Gautier was well-known as a frequent game show panelist, appearing on Match Game, Tattletales, Showoffs, You Don't Say!, Liar's Club, Password Plus, Body Language, Super Password, Win, Lose or Draw, and the TV version of Can You Top This? He also briefly tried his hand at emceeing on the early 1970s celebrity couples game It's Your Bet.
In 1972, when Burt Ward and Yvonne Craig reprised their Batman roles (as Robin and Batgirl respectively) for a TV public service announcement about equal pay for women, Adam West (who was trying to distance himself from the Batman role at the time) was absent. Instead, Gautier filled-in for West as Batman.
Gautier has performed several voice-over roles in animation, including Rodimus Prime in the third season of the Transformers animated series from 1986-1987 (taking over for Judd Nelson, who previously performed the role in the 1986 Transformers movie), as well as Serpentor in the G.I. Joe series. He was also narrator for Discovery Channel's Search for Adventure.
He is known for his caricatures of celebrities, and has written several instructional books on caricature, drawing, and cartooning.