The funnyman joined the likes of Beyonce, Kanye West, Rihanna and John Mayer at the Empire State of Mind hitmaker's exclusive in Las Vegas celebration, which served as the afterparty for his joint concert with Coldplay.
But an intoxicated Ansari was left red-faced when Jay-Z called him up to the stage to entertain attendees - and his mind went completely blank.
He explains, "I had one of the most humiliating, embarrassing things in my life happen to me.
"After the show there was this afterparty, at around 4.30 in the morning Jay-Z... goes, 'Yo Aziz, come up here and tell everyone a joke!' And I'm like, 'Argh! No!' and he kept pushing this, and it's 4.30 in the morning on New Year's Eve. (Jay-Z says), 'Yo, come up here and tell everyone a New Year's Day joke.'
"So I got up there and he passed me the mic and I'm like, 'Erm, OK, OK, yes... This one time, this restaurant came to my house. Hahaha, that didn't happen... I'm sleepy.'"
Ansari attempted to make amends minutes later and reached for the mic again to tell a joke - only to have his efforts shot down by the rap mogul.
He says, "I felt terrible, I felt like I'd let him down, so I was like, OK, let me think of something funny, and then I reached for the mic and he went, 'No! You had your chance and you missed it.' I was like, 'Oh no!' But I get it, he's Jay-Z. He's the smoothest man of all time."