Yang, who co-created the series with the former Parks and Recreation star and co-wrote "Parents," the episode which earned the award, spoke first when the pair accepted their golden trophy.
After getting out all of his thank yous, Yang made sure to share a poignant, funny point about Asian representation in American media, saying, "There's 17 million Asian-Americans in this country, and there's 17 million Italian-Americans. They have The Godfather, Goodfellas, Rocky, The Sopranos. We got Long Duk Dong, so we got a long way to go. But I know we can get there."
"Asian parents out there, if you could just do me a favor, if just a couple of you get your kids cameras instead of violins, we'll be all good," Yang joked, before passing the statuette to Ansari.
However, as Ansari stepped up to give his acceptance speech, it seems the producers assumed the pair had wrapped it up and began to play transitional music before the comic even took the mic.
It was clear there had been a mistake as Ansari tried to stammer over the music. For a moment, the music queued down as he said, "I just want to say-," but then it seemed as if he'd missed his chance and decided not to finish.
As Ansari seemed to savor the moment of embarrassment by awkwardly starting to run off stage, members of the audience tried to cheer him on and yelled at him to deliver his speech. The comic ran back and jokingly yelled to the producers, "Oh man! You guys are in trouble."
Ansari threw up his hands and jogged down the front steps of the stage, returning to his seat in the front row and Yang followed the presenters backstage. It was the kind of painfully awkward moment that would feel right at home in the comedy Ansari won the Emmy for in the first place.
Ansari got the chance to share a bit of his acceptance speech later in the show when he came out to present the nominees for Best Writing for a Variety Special.
"That was a little weird earlier," Ansari joked. "I just wanted to thank my parents, who are here. They inspired me that episode, for me."
"They acted in the show too," he continued. "My dad [was] very upset about his snub, but he'll be okay."
Backstage after the show, Ansari and Yang stopped to talk with ET's Kevin Frazier about their big win, and opened up about getting a ton of love and support from their families.
"My mom and dad both texted me really sweet, really funny things. Grammatically incorrect but very sweet," Yang joked. "I think my mom wrote, 'I'm very proud of you, it is a good speech.' Pretty straight to the point."
As for Ansari, he said his parents were making the most of their black tie evening.
"My parents are at some club. My dad is throwing an after party, invite only. It's a rival party to Kimmel's party. A lot of people are there. Game of Thrones people bailed on the HBO party, and they're at my dad's party," Ansari quipped. "No, they're somewhere [around here], lost."