The organization announced the award Monday during its 72nd annual voting meeting in Manhattan. Steven Sater and Duncan Sheik's "Spring Awakening" was named best musical.
Playbill said Stoppard's play recounts the tale of a group of 19th century Russian intellectuals in a trilogy. The plot revolves around political and philosophical debates, and efforts to reform the Russian political system. Each of the three sub-plays opened in succession during a two-month period.
Playbill said the late August Wilson's "Radio Golf" was named best American play.