Faber submitted Assuncao with a rear-naked choke at three minutes and 49 seconds of the third round.
"I'm ready to get that belt," Faber said. " We got a great champion right now. Jose Aldo. He's a phenom. He's both talented and creative. I'd love to go in there and get that belt."
"I respect Urijah but no one will take my belt," said titleholder Jose Aldo, who was invited in the cage to hype the matchup.
"I just got to bring my top game," Faber answered. "Like I said, he's a tough fighter, but in my mind, it's my belt."
The first round was competitive and could have gone either way, but Faber was the clear winner in rounds two and three.
In the second, Faber had a solid submission attempt on a guillotine choke and later floored Assuncao by clipping him with an overhand right when approached by a leg kick.
In the third, Faber took Assuncao down into halfguard. After standing back on his feet, Assuncao gained momentum by slipping Faber with a leg kick, but moments after, was put on his back courtesy of a straight right. Down on points, Assuncao took a chance to escape and had his back taken for the fight-ending rear-naked choke.
"It was a small mistake scrambling," Assuncao said. "I thought I would be able to get out of it, by giving up my back and controlling his wrist."
Faber improved to 23-3, while Assuncao fell to 14-2.