NEW YORK — On Broadway’s biggest night, a feel-good cross-dressing musical kicked up its heels.

“Kinky Boots,” the Harvey Fierstein and Cyndi Lauper show about a struggling shoe factory that turns to fetish-wear to survive, took home six awards, including the top prize of best musical during the 67th Tony Awards Sunday night at Radio City Music Hall.

While accepting the award for score, Lauper brought a bit of working-class charm to the ceremony with her trademark outer borough accent.

“It’s funny, you go around the world looking for acceptance — you forget that all you’ve got to do is look in your own backyard,” the veteran pop star told reporters backstage.

Entering the evening, the race for the top musical prize was considered too close to call between “Kinky Boots” and the dark British import “Matilda,” two springtime openings that had emerged as hits after little fanfare in the months leading up to their opening nights.

Still, “Matilda, the Musical” performed decently, winning four Tonys from its 12 nominations, including book for Dennis Kelly.

Perhaps most unexpectedly, the night was marked by a series of big wins for the revival of Edward Albee’s marital drama “Who’s Afraid of Virginia Woolf?” A half-century after being introduced to the American stage, the show took home Tonys for revival of a play, director of a play and, in the upset of the night, actor in a play, given to Tracy Letts over Tom Hanks, star of the late Nora Ephron’s journalism tale “Lucky Guy.”

Letts, who in 2008 won a Tony for best play for his drama “August: Osage County,” is now part of an elite group that has won Tonys for both writing and acting. Another member? “Kinky Boots” scribe Fierstein, who has won both actor and play Tonys for “Torch Song Trilogy,” an acting prize for the musical “Hairspray” and a book award for the musical “La Cage Aux Folles.”

One of the most compelling narratives Sunday night had less to do with a particular winner and a lot more to do with the tenor of the overall honorees.

As Hollywood continues to be the subject of criticism for a lack of inclusiveness, 2013 was an extraordinarily good year for both women and minorities on Broadway. African-American actors won four of the eight acting Tonys: lead actor in a musical for Billy Porter (“Kinky Boots”), lead actress in a play for Cicely Tyson (“The Trip To Bountiful”), lead actress in a musical for Patina Miller (“Pippin”) and featured actress in a play for Courtney B. Vance (“Lucky Guy”).

Tyson, who made her return to Broadway after 30 years away, gave a deliberate, emotional speech that evoked the specter of dead family members. Porter was more quippy.

“I share this award with you,” he said to “Kinky Boots” co-star and fellow nominee Stark Sands. “I’m going to keep it at my house, but I share it with you.”

Lauper was the first woman to win a best score Tony on her own, without sharing the award with a man. And winners for both director of a musical and director of a play were women, “Pippin’s” Diane Paulus and “Virginia Woolf’s” Pam MacKinnon.

Though “Virginia Woolf” opened in the fall and closed months ago, it has managed to emerge as a force during Tonys season even as many anticipated dramas that opened later — including “Orphans,” “Breakfast at Tiffany’s” and “Cat on a Hot Tin Roof” — faltered.

Asked Sunday about the staying power of his show, Letts said that the production, an import from Chicago’s Steppenwolf Theatre, owed its resilience to the work itself.

“It’s a testament to Edward Albee’s play,” he said. “It sticks to the ribs.”

On stage, Letts played down the competition between himself and Hanks and the other nominees. “You are not my competition, you are my peers, and I am proud to be in your company,” he said. Hanks was a crowd favorite in Radio City Music Hall, and his defeat was seen as a surprise after a Tonys season that had seen much mutual affection between the star and the Broadway community.

Though there had been much hype about “Lucky Guy,” the creation principally of two theater outsiders in Hanks and Ephron, neither was handed prizes Sunday night. And many Hollywood actors, such as Sigourney Weaver and Scarlett Johannson, were not even nominated this year. Instead, Tonys voters reserved honors for many longtime theater insiders, including Letts, Paulus and Christopher Durang.

Durang’s dysfunctional-family comedy “Vanya, Sonia, Masha and Spike” was named best play, besting Ephron’s “Lucky Guy” and marking Durang’s first-ever Tony. He noted the passage of time in accepting the prize.

“I wrote my first play in second grade in 1958,” Durang said. “It’s now 2013.”

While “Virginia Woolf” was one of the most critically lauded shows of the season, “Kinky Boots” has been more popular with ticket buyers. The show is likely to reap the commercial rewards that come with a best musical win; it will tour beginning in 2014.

Longtime Broadway producer Daryl Roth acquired rights to the obscure British movie it was based on more than seven years ago. She said before the Tonys that she felt the nominations validated her choice to make a show out of the film when few had heard about it.

“There was something about this story that spoke to me, and it’s hugely gratifying to see it’s speaking to theatergoers too,” she said.

Accepting his own prize, “Matilda’s” Kelly said he wasn’t quite sure what he was getting into when he began writing the show. “I had no idea how to write a musical. So in many ways this award is a ringing endorsement of ignorance and stupidity,” Kelly said.

With many of the season’s biggest hits still new and relatively unknown, producers saw fit to pay tribute to big musicals.

The opening number included an homage to nearly every musical running on Broadway, including longtime hits such as “The Lion King” and “Chicago.” The number brought the Radio City audience to its feet.

Meanwhile, performers from established shows such as “Newsies” and “Jersey Boys” introduced new shows, while “Phantom of the Opera” earned a stand-alone tribute in honor of its 25th anniversary.

Neil Patrick Harris hosted the event for the third consecutive year, as the CBS telecast aimed to goose its numbers above the two-decade low last year, when only 6 million people tuned in.

Tonys speeches tend to be theatrical affairs. They were marked most notably Sunday by an earnest speech from Judith Light, who took home featured actress in a play for her turn in Richard Greenberg’s drama “The Assembled Parties,” and a free-associative speech from “Pippin” star Andrea Martin. Accepting the prize for featured actress in a musical, Martin, 66, cited a co-star who tossed her in the air. She asked the audience if they knew how special it is for “a woman of my age to be held and never dropped.”

(Meredith Blake and Alana Semuels contributed to this report.)

Distributed by MCT Information Services

 Note: An earlier version of this story requires correction. Martin won the award for “Pippin,” not “Kinky Boots.” It has been corrected.