Cooper won both the Tony and Drama Desk Award for her performance as Jan Donovan in Woman of the Year, a role she recreated in the musical's television version. She appeared in the original Broadway productions of West Side Story and Gypsy, and her many other Broadway credits included Hallelujah, Baby!, I Can Get It For You Wholesale, Two By Two, On The Town, Ballroom, Grease, and the female version of The Odd Couple.

She also guest starred on numerous television shows including Alice, The Nanny, and Law & Order.