Brown took home the Golden Globe for Best Performance by an Actor in a Television Series Drama for his work on This is Us, the first black man to win the award.
"You wrote a role for a black man that could only be played by a black man, and what I appreciate so much about this thing is I'm being seen for who I am and being appreciated for who I am," Brown said during his acceptance speech where he thanked This is Us creator Dan Fogelman.
"And it makes it much more difficult to dismiss me or anyone who looks like me," he continued.
Ansari then became the first Asian man to win the award for Best Performance by an Actor in a Television Musical or Comedy for Master of None.
"I genuinely didn't think I was gonna win cause all the websites said I was going to lose," the comedian said onstage. "The only reason my acting is good in that show is because everybody else holds me up."
"In 1982, Sidney [Poitier] received the Cecil B. DeMille Award right here at the Golden Globes," she said.
"It is not lost on me that at this moment, there are some little girls watching as I become the first black woman to be given this same award."