Hurst was born in Brooklyn, New York. She graduated from Mount Holyoke College in 1974. She began her career in theatre, and in the 1990s began appearing in television and film. Hurst is known for her multiple roles in various Law & Order television shows. She co-starred in films like Airheads, Smoke, Stepmom and Sherrybaby.
Hurst starred as Miss Claudette Pelage in the first season of the Netflix comedy-drama series, Orange Is the New Black in 2013. This role earned Hurst, along with the main cast, a Satellite Award for Best Cast – Television Series. She left the show after a single season. On Christmas of 2013, she was seriously injured in a car accident. Hurst was placed in a 16-day coma so doctors could perform surgeries close to her spine.
In January 2015 Hurst appeared in the third series of the British television drama series Last Tango in Halifax.
