She was born in New York City to a Jewish family whose surname was originally "Woronoff". Beginning her career as a ballet dancer, she trained at the School of American Ballet, entering the Actors Studio at the age of seventeen - reputedly the youngest applicant ever to be accepted. She made her Broadway debut in 1963 in the musical, 110 in the Shade. Having failed to obtain the role of Liesl in the film version of The Sound of Music, her first major success was in the title role of Rodgers and Hammerstein's television special, Cinderella, in 1965. She later replaced Barbara Bain as the leading female in the Mission Impossible team.

In 1967, she married producer Jon Peters, and they had one son, Christopher, who became an actor, but were later divorced. Her numerous film appearances include The Happiest Millionaire (1967), Cat Ballou (1971), Victor/Victoria (1982), and famous Miss Scarlet in Clue.

She has also appeared extensively on television. Most recently, she has had recurring roles on Will & Grace - as Will's father's mistress - and on Desperate Housewives as Susan's mother.