The comedy partners received the Best Musical prize at the 77th annual ceremony in New York on Friday (20May11).
Parker and Stone have struck gold with their hit show, about two young Mormon missionaries who are sent to Uganda to promote the faith, which has been nominated for a string of top Broadway honours, including 14 Tony awards.
Meanwhile, the Drama League hailed War Horse as the Best Play, while actor Mark Rylance went home with the Distinguished Performance Award for his performance in Jerusalem.
Rylance saw off competition from Hollywood stars including Al Pacino, Daniel Radcliffe and Vanessa Redgrave to scoop the prestigious honour - the night's sole acting prize.
Previous recipients of the Distinguished Performance Award include Liam Neeson, Hugh Jackman, Patti LuPone, Glenn Close, Liev Schreiber and Sir Ian McKellen.