The last to win the award was Andre Braugher in 1998 for his role in "Homicide: Life on the Street".
"I just want to say Mr Braugher, whether at Stanford University or on this Emmy stage, it is my supreme honour to follow in your steps," Brown said, before pivoting to thanking his TV family.
"Milo, Mandy, Justin, Chrissy - you are the best white TV family that a brother has ever had. Better than Mr. Drummond, better then them white folks at Webster," he added.
"You can play. You can play," he said to the Emmys' house band. "Nobody got that loud music."
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After his mic was turned off, the 41 year-old actor tried to finish his speech to the cheers of the Microsoft Theater audience, but the attempt proved unsuccessful, reported Variety.
A reporter backstage asked the actor if he would like to finish his acceptance speech and he happily obliged.
"I wanted to thank Dan Fogelman - he is the Hebrew hammer with which our house was built. He makes me laugh and cry in equal parts and keeps me coming back for more, and in his own little small special way...I wanted to thank my manager. And to my wife - I didn't get to thank my wife - you make my life worth living and you gave me two of the most beautiful things that God has ever put on this planet. Your daddy loves you with the strength of 1000 suns," he said.
This was the second Emmys win for the 41-year-old actor, who took home a supporting-actor trophy last year for his breakout role in Ryan Murphy's "The People v O J Simpson", which helped turn him into a household name.