The prizes will be presented at the organization's 62nd annual awards ceremony May 24 at Sardi's Restaurant in Manhattan.
"Guvnors" won the honors for Outstanding New Broadway Play, Outstanding Director of a Play for Nicholas Hytner and Outstanding Actor in a Play for James Corden.
"Once" was declared Outstanding New Broadway Musical and also took the prizes for Outstanding Book of a Musical and Outstanding Director of a Musical for John Tiffany.
"Sons of the Prophet" won the award for Outstanding New Off-Broadway Play, "Queen of the Mist" for Outstanding New Off-Broadway Musical, "Death of a Salesman" for Outstanding Revival of a Play and "Follies" for Outstanding Revival of a Musical.
Winning the Outstanding Actress in a Play prize was Tracie Bennett from "End of the Rainbow." Danny Burstein won the Outstanding Actor in a Musical award for "Follies," while Audra McDonald was named Outstanding Actress in a Musical for "Porgy and Bess."