Giles Terera scored the prize for Best Actor in a Musical, while his co-star Michael Jibson earned the accolade for Best Supporting Actor in a Musical. "Hamilton" also won for Best Music, Lighting Design, Sound Design and Choreography.
Miranda, who created and starred in the original Broadway cast of Hamilton, did not attend the ceremony after announcing last week he is suffering from shingles.
Shirley Henderson from "Girl from the North Country" was deemed Best Actress in a Musical and her cast-mate Sheila Atim was voted Best Supporting Actress in a Musical.
"Follies" won the prizes for Best Revival of a Musical and Best Costume Design.
"Angels in America" was declared Best Revival of a Play and cast member Denise Gough picked up the statuette for Best Supporting Actress in a Play.
"The Ferryman" earned the title of Best New Play and Sam Mendes took home the Best Director trophy for helming it. The Best Actress honor was presented to the drama's lead Laura Donnelly.
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