A seven-time Tony Award nominee, Burstein won the 2020 Tony Award for Best Featured Actor in a Musical for his performance as Harold Zidler in Moulin Rouge! on Broadway. His Tony-nominated roles were in The Drowsy Chaperone (2006), South Pacific (2008), Follies (2011), Golden Boy (2013), Cabaret (2014), and Fiddler on the Roof (2016). Other notable Broadway credits include The Seagull (1992), Saint Joan (1993), and Women on the Verge of a Nervous Breakdown (2010), and Pictures From Home (2023).