Grier won in the best-featured actor category for his role in the Pulitzer Prize-winning A Soldier's Play, which focuses on Black soldiers in World War II.
He made a joke during his speech to Tony-winning actress Audra McDonald, who served as one of the evening's hosts. "Audra, I finally won one of these too!" he said. He also thanked his director, Kenny Leon, for casting him in the play.
"I'm just glad you called," he said.
He also joked with the other nominees in the category, saying, "And to the other nominees, tough bananas! I won!"
Adrienne Warren also won as best actress for her role as Tina Turner in Tina - The Tina Turner Musical.
Warren thanked her parents for supporting her throughout her career. "Everything I am is because of you," she said. She also thanked Turner "for trusting me to bring her story home."
Moulin Rouge: The Musical won 10 Tonys Sunday night, boxing out Jeremy O. Harris' Slave Play, which was expected to win at least one of its 12 nominations, according to Variety. Diablo Cody also won for best book for Jagged Little Pill. The Inheritance won Best Play. Theatrical producer Irene Gandy, author Beverly Jenkins and New Federal Theater founder Woodie King Jr. were Black theatrical icons among those honored for excellence in theater.