Prince was born in Augusta, Georgia, and raised in Lynchburg, Virginia, where she attended E.C. Glass High School, and later studied theater at the Cincinnati Conservatory of Music. She made her Broadway debut as the Gypsy character Tessie Tura in Jerome Robbins' Broadway (1989) and followed this with a role in the ill-fated Nick & Nora.
She established herself as a Broadway star with her portrayal of Miss Adelaide in the 1992 revival of Guys and Dolls, for which she won both the Tony and Drama Desk Award as Best Actress in a Musical. In 2001, Prince was once again nominated for Tony and Drama Desk Awards for her portrayal of Ella Peterson in the 2001 revival of Bells Are Ringing. She was featured in the 2008 Broadway musical A Catered Affair, for which she received Tony and Drama Desk nominations.
She appeared in a concert version of Sweeney Todd with the Orlando Philharmonic Orchestra in Orlando, Florida in March 2009. On April 7, 2009, she took over the role of Ursula from Heidi Blickenstaff in the Broadway musical The Little Mermaid.
She appeared in such films as The Last Dragon (1985), Dave (1993), Picture Perfect (1997), and Our Very Own (2005), among others. Her television credits include the short-lived High Society (1995); recurring roles on Spin City (1997–2000) and Huff (2004–2005), as well as guest appearances on such shows as Remington Steele, Law & Order, Monk, Frasier, House, Grey's Anatomy, Drop Dead Diva, Ugly Betty, and Happy Endings.
A live recording of her 2005 cabaret debut at Joe's Pub, at The Public Theater, entitled A Leap of Faith, was released on the DRG Records label. A second recording, titled Total Faith was recorded at the Royal Room, Palm Beach, Florida. She has participated in studio recordings of scores from Breakfast at Tiffany's and Jerry Herman's unproduced musical, Miss Spectacular.
She performs her cabaret act in various venues, such as the Orange County Performing Arts Center, California, in April 2010 and Caramoor, New York, in May 2010. Prince appeared in the concert version (and accompanying recording) of the revue Life Begins at 8:40 at the Library of Congress in Washington, DC, on March 22, 2010. She also performed the closing show in the 2002-2003 theatre season at Eisenhower Hall at West Point.
Prince played Mrs. Wilkinson in the second United States national tour of Billy Elliot the Musical, which began performances in October 2010 and ended in August 2011.
She returned to the Broadway stage replacing Jane Lynch as Miss Hannigan in the revival of Annie as of July 19, 2013.