The show rose to a strained moment in American history with warmth, grace and a vindication of theater’s special skill for bringing people together.

Ari’el Stachel, a surprise winner as best supporting actor for his performance in “The Band’s Visit,” spoke movingly about the power of living one’s ethnic identity honestly onstage. His castmate Tony Shalhoub, accepting a Tony as best actor in a musical, spoke of his father’s arrival at Ellis Island (from Lebanon) 100 years ago.