"God of Carnage" won the league's top prize for a play, while "Hair" took the revival of a musical honor and "Blithe Spirit" the revival of a play accolade.
Australian actor Geoffrey Rush won the distinguished performance award for his work in the play "Exit the King."
The awards were presented at the 75th annual Drama League Awards ceremony and luncheon at the Marriott Marquis Hotel in Manhattan's Times Square.
Jeremy Irons and Cynthia Nixon served as co-hosts of the event.
2014: The Year in Music [PHOTOS]