Award presenter Chris Rock joked there was so little suspense surrounding the night's top prize that reading the names of "Mormon's" fellow nominees was "like taking a hooker to dinner."
The edgy stage show from Matt Stone and Trey Parker, the creators of TV's animated "South Park," features extensive profanity and scatological humor. It went into the weekend's Tony race with 14 nominations.
"Mormon" tells the story of how two missionaries try to convert Ugandan villagers facing poverty and strife unlike anything the naive visitors could imagine. While one of the young men in overwhelmed, the second attempts to teach the villagers about God in a way to which they can relate, inspiring them to hope for better lives.
"Thank you. This has been really, really cool," Parker said as he took the stage to collect the Best Musical trophy. "We really want to thank the audiences because you guys made this show what it is and, therefore, you are going to have to atone for it one day. It's yours now. It's your responsibility ... . I think the night would be a big disappointment if we didn't thank our co-writer who passed away, Mr. Joseph Smith, the founder of the Mormon religion. He couldn't be here tonight, but you did it, Joseph. You got the Tony."
One of the show's few female cast members, Nikki M. James, picked up the statuette for Featured Actress in a Musical earlier in the evening.
"Tony, come on over and live with me. I didn't expect to be standing here tonight. I tried to write a speech, but I just felt silly," James said.
"Mormon" also garnered the awards for Best Book of a Musical, Best Direction of a Musical, Best Sound Design of a Musical, Best Scenic Design of a Musical, Best Lighting Design of a Musical, Best Orchestrations and Best Original Score.
"War Horse" won the honors for Best Play, Best Direction of a Play, Best Scenic Design of a Play and Best Sound Design of a Play.
John Benjamin Hickey and Ellen Barkin won the trophies for Featured Actor and Actress in a play for their supporting roles in "The Normal Heart." The drama also scored the title of Best Revival of a Play.
"Anything Goes" won the statuettes for Best Revival of a Musical, Best Choreography and Best Actress for Sutton Foster.
John Larroquette earned the award for Featured Actor in a Musical for "How to Succeed in Business Without Really Trying," Frances McDormand was named Best Actress in a Play for her work in "Good People," Mark Rylance garnered the gong for Best Actor in a Play for his performance in "Jerusalem" and Norbert Leo Butz picked up the prize for Best Actor in a Musical for "Catch Me If You Can."
Actor Neil Patrick Harris served as host of the event at Manhattan's Beacon Theatre.
2014: The Year in Music [PHOTOS]