It was nominated for a record-breaking 16 awards during Sunday's prizegiving.
In addition to the top award presented to them by Barbra Streisand, the show's star, creator and lyricist Lin-Manuel Miranda, took best book of a musical and best original score.
Miranda lost the best leading actor in a musical trophy to his co-star Leslie Odom, Jr, while other acting prizes went to Renee Elise Goldsberry (best featured actress in a musical) and Daveed Diggs (best featured actor in a musical).
Although "Hamilton" went home with 11 trophies, it did not break the record for the most wins in one night, which is held by "The Producers."
The musical was honoured with 12 Tonys in 2001.
Meanwhile, acclaimed show "The Humans" scored the most trophies in the play categories, for best play, best featured actor and actress prizes for its two stars Reed Birney and Jayne Houdyshell, respectively, and best scenic design of a play for David Zinn.
Arthur Miller's "A View From The Bridge" was given two Tonys, for best revival of a play and for its director Ivo van Hove.
Casts from each of the best musical contenders - "Bright Star", "Hamilton", "School of Rock", "Shuffle Along" and "Waitress" - treated viewers to song and dance numbers, while stars from best revival of a musical nominees, "The Color Purple", "Fiddler on the Roof", "She Loves Me" and "Spring Awakening", also hit the stage to perform.
The ceremony held at New York City's Beacon Theatre, was hosted by James Corden, who in his monologue, addressed the tragic Orlando shooting.
Also during the show, the American Theatre Wing - which hands out the Tonys - announced its new Andrew Lloyd Webber Initiative, which is being funded with a USD 1.3 million, three-year grant from Lloyd Webber, that will support theatre education opportunities for under-resourced public schools around the United States.
