'Kinky Boots' - which won a total of six Tonys - was named 'Best Musical', and its star Billy Porter won 'Best Performance by an Actor in a Leading Role in a Musical.
Cyndi Lauper beat nominees including 'Matilda's' Tim Minchin in the race for the 'Best Original Score' prize, and the musical - based on the story behind the 2005 movie of the same name - also took home awards for choreography, sound design and orchestration.
The Grammy award-winning musician later returned to the stage for a performance during the ceremony's 'In Memoriam' segment.
Pulitzer Prize winner Tracy Letts beat Tom Hanks, Tom Sturridge, David Hyde Pearce and Nathan Lane to win 'Best Performance by an Actor in a Leading Role in a Play for 'Who's Afraid of Virginia Woolf?'
The Edward Albee drama also took home the prize for 'Best Revival of a Play', while its director Pam MacKinnon was also recognised with an award.