McDonald, 43, who topped Angela Lansbury and Julie Harris's previous records of five acting Tonys each, openly wept as she received a prolonged standing ovation.
Her latest win - for Best Lead Actress in a Play for portraying Billie Holiday in "Lady Day at Emerson's Bar & Grill" - also made McDonald the first person ever to win in four different performance categories.
She previously won as Best Featured Actress in a Play ("A Raisin in the Sun" and "Master Class"), Best Lead Actress in a Musical ("The Gershwins' Porgy and Bess") and Best Featured Actress in a Musical ("Ragtime" and "Carousel"). She also has two Grammys.
The moment was not lost on McDonald, who first thanked her parents, both deceased, for "disobeying doctors' orders and not medicating their hyperactive girl, and finding out what she was into instead and pushing her into the theater."
She then thanked her new husband and "best friend," fellow Broadway actor Will Swenson, calling him, "the best supporter I've ever known."
After acknowledging her two stepsons, she turned to face her daughter, Zoe, sitting in the audience, and said, "Without you, I am nothing. Do you understand, mommy is nothing without you."
McDonald concluded her speech with an acknowledgement of "all the shoulders of the strong and brave and courageous women I am standing on."
As the audience cheered, McDonald rattled off the names Lena Horne, Diahann Carroll, Ruby Dee, Maya Angelou and Billie Holiday.
Watch the full speech below: