Helen Mirren won her first Tony on Sunday for her role as Queen Elizabeth II in The Audience, and the lesbian coming-of-age story Fun Home nabbed the top acting prize for Michael Cerveris and best musical at the 69th Tony Awards.

British import The Curious Incident of the Dog in the Night-Time, about a teenage math wizard with Asperger Syndrome who goes on an incredible journey, won five awards, including best play, director and actor for its star, recent Juilliard School graduate Alex Sharp.

Mirren described her win as “an incredible honour”.

With a Tony, Broadway’s highest honour, an Emmy and an Oscar, she said she would love to win a Grammy, which are for recorded material. “I have to do an audio book,” she joked.

Sharp, in his Broadway debut, surpassed Hollywood star Bradley Cooper and veteran actor Bill Nighy for the best actor accolade.

“Oh my God, oh my God. It’s so crazy,” said a surprised Sharp, who dedicated his award to young people who feel misunderstood or different.

Cerveris took home best actor in a musical, his second Tony, for playing the closeted homosexual father in Fun Home, which also earned Tonys for best director for Sam Gold, as well as best book and best score.

“I am fortunate to be standing here. You all deserve to be,” he said to his fellow nominees. “Our show is about home and finding who you are.”

After six nominations, Kelli O’Hara took home her first Tony for best actress in a musical as the governess in The King and I.

The three-hour show capped a record-breaking season on Broadway

“You would think that I would have written down something by now but I haven’t,” a jubilant O’Hara said, thanking her husband and parents. “I’m going to do the worm,” she said as she began to dance.

Past winners Kristin Chenoweth and Alan Cumming co-hosted the ceremony, which was broadcast live on CBS television and featured songs from top musicals.

The three-hour show capped a record-breaking season on Broadway in which audience numbers topped 13.1 million and ticket grosses rose to $1.36 billion.

Skylight won best revival of a play and The King and I took best revival of a musical.

Ruthie Ann Miles, who won the best featured actress in a musical Tony, consulted her cell phone on stage as she accepted the honour.

Mirren’s co-star Richard McCabe picked up the best featured actor prize in a play.

A tearful, flustered Annaleigh Ashford was named best featured actress in a play for her role as the zany ballet-dancing daughter in an eccentric American family in You Can’t Take it With You.

Christian Borle won his second Tony for best featured actor in a musical, for Something Rotten!

“This feels like an embarrassment of riches,” said Borle about his portrayal of William Shakespeare as a rock star in the bawdy parody of Broadway musicals set in 1590s Tudor England.

The Tony Awards are presented by theatre industry association The Broadway League and the American Theatre Wing, a not-for-profit organisation.

Main winners

Best musical
Fun Home

Best play
The Curious Incident of the Dog in the Night-Time
Simon Stephens

Best revival of a musical
The King and I

Best revival of a play
Skylight

Best performance by a leading actress in a musical
Kelli O’Hara, The King and I

Best performance by a leading actor in a musical
Michael Cerveris, Fun Home

Best performance by a leading actor in a play
Alex Sharp, The Curious Incident of the Dog in the Night-Time

Best performance by a leading actress in a play
Helen Mirren, The Audience

Best direction of a musical
Sam Gold, Fun Home

Best direction of a play
Marianne Elliott, The Curious Incident of the Dog in the Night-Time

Best book of a musical
Fun Home, Lisa Kron

Best original score
Fun Home, Jeanine Tesori, Lisa Kron

Best choreography
An American in Paris