A tearful McDonald thanked her "mom and dad up in heaven" and closed with, "This is for you, Billie."
In the revival, which is running at the Circle in the Square Theatre, McDonald plays the doomed Holiday as she tries to make it through a concert despite health problems. (In real life, the singer was a heroin addict and alcoholic.)
With Sunday's win, McDonald has a total of six Tonys, with at least one win for each actress category (lead and featured, play and musical). She is now tied with the late Julie Harris for the actress with the most Tony Awards. (Harris won five competitive Tonys and received a special career Tony in 2002.)
This year's other nominees were Tyne Daly for "Mothers and Sons," LaTanya Richardson Jackson for "A Raisin in the Sun," Cherry Jones for "The Glass Menagerie," and Estelle Parsons for "The Velocity of Autumn."
Last year's winner was Cicely Tyson in a revival of "The Trip to Bountiful." Tyson will reprise her role in the Horton Foote drama at the Ahmanson Theatre in Los Angeles, with performances set to begin Sept. 17.