The Producers has broken the old Tonys record of 14 nominations, set by Company, in 1971.
It also garnered more than 80 major prizes, including Oliviers, Tonys and Evening Standard awards.
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In a statement, Harris said he was excited to be back hosting the Tonys, adding: "The show will rock!"
Judy Kaye and Michael McGrath received best supporting actors in a musical Tonys.
The original production of South Pacific - composed by Richard Rodgers and Oscar Hammerstein II - won nine Tonys in 1950.
The production, which features music from pop singer Cyndi Lauper, is expected to be nominated for best musical at this year's Tonys.
The original production starred two rising musical theater stars: Norbert Leo Butz, who has since won two Tonys, and Sherie Rene Scott.
Harris previously hosted the Tonys last year and in 2011 and 2009.
The penthouse apartment has ceilings befitting a man of his height, with a very tall shelf in one corner housing his nine Tonys.
That revivals are currently the toast of the town means nothing to the plays' producers when the Tonys are announced early next month.
Certainly, limo dispatcher Sebastian Lazaro gives the Mamet play--which features Alan Alda, Liev Schreiber and Gordon Clapp, all of whom are up for Tonys--his own personal rave.
After the ceremony, Daldry said that he was a "happy bunny" and "genuinely thrilled" that the musical had been accepted on Broadway and celebrated at the Tonys.
Her revivals of both "Hair" and "The Gershwins' Porgy and Bess" have not only gone to Broadway but have won Tonys for best revival of a musical.
When you get to my age, you just get to a point where you stop listening to the Tonys and you just assume you're not going to be nominated.
Last June, the Matijcios were proud when friends told them that "a large part of the Ukrainian community in New York were watching the Tonys, " rooting for their daughter.
It stars Nathan Lane and Matthew Broderick, both of whom are nominated for the best actor in a musical award at the Tonys, which honour the best of the Broadway season.
Hollywood producers used to jump at the opportunity to turn a successful musical into the next blockbuster West Side Story and The Sound of Music were winning Tonys long before they won Academy Awards.
But if results from many of the year's other award shows, including the Tonys, the Grammys and the Academy of Country Music Awards, are any indication, the Tiffany network has reason to be hopeful.
The live broadcast of the Tonys at the Beacon Theatre began with a performance from the cast of "The Book of Mormon" and reliably charming opener by host Neil Patrick Harris, who kept the show moving along at a pace from which the Academy Awards could learn.
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