A Strange Loop, the story of a black gay man and his mental struggles as a playwright, took the Best Musical honour at a live ceremony held at Radio City Music Hall in New York.
Strange Loop triumphed over MJ, a crowd-pleasing musical about Michael Jackson. Star Myles Frost won best actor in a musical for playing the King of Pop.
Being on stage to accept the Tony felt like a "miracle", said Ben Power, the writer of Lehman Trilogy, after Covid-19 halted preview shows of the play, for 577 days.
"In New York, even after everything, even after today, anything is possible," Power said, also saying that the play had been written as "a hymn to the city of New York".
Simon Russell Beale, the star of Lehman Trilogy, won the Tony for lead actor in a play. Joaquina Kalukango took best actress in a musical for Paradise Square.
For Best Revival of a Musical, Tony voters honoured Company, the final project backed by composer and theatre legend Stephen Sondheim, who died in November.
The new Company reverses the gender roles of the original, which centred on a single man considering his life choices as he turned 35. Producer Chris Harper thanked Sondheim "for letting us re-imagine the classic musical".
Patti LuPone won her third Tony Award for a supporting role in Company and thanked, among others, "all of the Covid safety people" for making Broadway's return possible. In the audience were 150 Covid-19 safety managers who had kept shows running.
Best Revival of a Play went to Take Me Out, the story of a gay baseball player.
Deirdre O'Connell won the Tony for lead actress in a play for Dana H. As she accepted her trophy, she encouraged aspiring writers to "make the weird art".
List of winners in key categories
The Lehman Trilogy
A Strange Loop
Best Revival of a Musical
Best Revival of a Play
Take Me Out
Best Performance by an Actor in a Leading Role in a Play
Simon Russell Beale, The Lehman Trilogy
Best Performance by an Actress in a Leading Role in a Play
Deirdre O'Connell, Dana H
Best Performance by an Actor in a Leading Role in a Musical
Myles Frost, MJ
Best Performance by an Actress in a Leading Role in a Musical
Joaquina Kalukango, Paradise Square
Best Original Score
SIX, Toby Marlow and Lucy Moss
Best Book of a Musical
A Strange Loop, Michael R Jackson