The show also earned the prizes for Best Director of a Play for Kenny Leon and Best Featured Actress in a Play for Sophie Okonedo.
"This is the most amazing cast in the world. Every night at the Barrymore [Theatre] because they sit on the stage and they listen to each other. They listen to each other," Leon said as he collected the play's final award.
He then declared Scott Rudin "one of the best producers in the business," saying he "gives artists everything we need to succeed."
"Denzel [Washington] is our anchor, but LaTanya Richardson Jackson is the glue and I want to thank you, LaTanya, for stepping in and just delivering a wonderful, wonderful performance," Leon added.
Jackson replace Diahann Carroll, who withdrew from the production while the show was still in rehearsals.
Notable deaths of 2014 [PHOTOS]