Among many national tours, Rivera starred most notably in "Sweet Charity" directed by Bob Fosse, playing the role of Nickie in the film adaptation of "Sweet Charity " with Shirley MacLaine (1969). Rivera appeared three times on "The Hollywood Palace", twice on "The Carol Burnett Show" (including an episode airing February 22, 1971) and between 1973–74, played Connie Richardson on "The New Dick Van Dyke Show". In 1975, she earned a Tony Award nomination starring as Velma Kelly opposite Gwen Verdon in the original cast of the musical "Chicago", directed by Bob Fosse. In addition to her ballet instructors, Rivera cites Leonard Bernstein and Verdon, with whom she starred in "Chicago", as influential to her success. She later made a cameo appearance in the 2002 movie version. She appeared as Fastrada in a filmed-for-television version of the musical "Pippin" in 1981, and was nominated for Tony and Drama Desk Awards for "Bring Back Birdie" (1981) and a Tony Award for "Merlin" (1983) on Broadway.