"Clybourne Park" was declared Best Play, "Porgy and Bess" Best Revival of a Musical and "Death of a Salesman" Best Revival of a Play.
In addition to the top musical prize, "Once" also scooped up the awards for Best Direction of a Musical, Best Book of a Musical, Best Orchestrations, Best Sound Design of a Musical, Best Lighting Design of a Musical and Best Scenic Design of a Musical.
The show's leading man, Steve Kazee, snagged the trophy for Best Actor in a Musical and dedicated it to his mother, who died of cancer in April. He offered his heartfelt thanks to his fellow cast members for helping him through his grief, as well.
"My mother always told me before shows to 'stand up there and show them whose little boy you are.' And I'm showing you today that I am the son of Kathy Withrow Kazee, who lost her fight with cancer on Easter Sunday this year and I miss you every day and I feel you here with me here tonight and I love you all so much and thank you for this award," Kazee said.
James Corden also gave an emotional acceptance speech as he collected the Tony for Best Actor in a Play for his work in the British slap-stick comedy "One Man, Two Guvnors."
"I am overwhelmed," Corden said. "The audiences here have embraced our show like we never, ever imagined they could. Every night is a joy."
At a ceremony dominated by first-time winners such as Kazee and Corden, Audra McDonald scored her fifth Tony Award for her moving performance in the tragic love story "Porgy and Bess."
"I was a little girl with a pot belly and Afro puffs, hyperactive, and I found the theater and I found my home and a place to express myself and I was so grateful, even at the age of 9, and, to think the theater would be so good to me, is mind-blowing. I'm so grateful to be a part of this company," said McDonald, winner of the Best Actress in a Musical Tony Award.
"Peter and the Starcatcher," a Peter Pan inspired story, was also a big winner Sunday night. Christian Borle won the Tony for Best Supporting Actor in a Play for his portrayal of the outrageous pirate Black Stache, while the show earned the awards for Best Scenic Design of a Play, Best Sound Design of a Play, Best Lighting Design of a Play and Best Costume Design of Play.
The Tony for Best Direction of a Play went to Mike Nichols for "Death of a Salesman."
"This was my neighborhood movie theater when I was a kid. I once -- at a Saturday kids' matinee -- won a pie-eating contest. It was nice, but this is nicer. You see before you a happy man," Nichols, a six-time Tony Award winner for directing, said of this year's Tonys venue, the Beacon Theatre. "I have to thank Rebecca Miller because she trusted us to do Arthur Miller's greatest play and I got to do his play and I got to do it with a cast straight from heaven. ... I can't talk about them. I love them too much."
"Other Desert Cities" star Judith Light won the prize for Best Supporting Actress in a Play, while "Nice Work if You Can Get It" co-stars Michael McGrath and Judy Kaye went home with matching statuettes for Best Supporting Actor and Actress in a Musical. Nina Arianda earned the Best Actress in a Play title for her work in "Venus in Fur," and "Newsies" won Best Choreography and Best Original Score honors.
Neil Patrick Harris served as the host of the 3-hour-long Tony Awards show, which aired on CBS.
Celebrity Families of 2014 [PHOTOS]