In 1951, Rivera accompanied a friend to the audition for the touring company of "Call Me Madam" starring Elaine Stritch and ended up winning the role herself. She followed this by landing roles in other Broadway productions such as "Guys and Dolls", "Can-Can", "Mr. Wonderful" starring Sammy Davis, Jr., and "Seventh Heaven" and dancing on "The Maurice Chevalier Special" in 1956. In 1957, she was cast in the role which was destined to make her a Broadway star, the firebrand Anita in "West Side Story" (the role would bring fame and an Oscar to another actress of Puerto Rican descent, Rita Moreno, in the 1961 film version).