Northcutt (6-0) took advantage of a Trevino slip early in the fight. As Trevino scrambled back to his feet, Northcutt unleashed a barrage of punches that backed his opponent to the fence.
As Trevino (12-2) raised his arms in defense, Northcutt changed levels for an easy takedown. After putting Trevino on his back, he dropped elbows to the head until referee Herb Dean stopped the fight.
Trevino, who missed weight for the fight, protested the stoppage but made it clear to everyone in the building he was finished.
Northcutt, a student at Texas A&M University, is the third-youngest athlete to ever debut for the UFC. He trained karate since he was four and has competed in international tournaments from a young age.
"This feels amazing, it's such an honor to be here," Northcutt said. "The crowd, everyone around the UFC, were all amazing and this was just an incredible experience. I've been training for this since I was four.
"The fight went just how I visualized it. I thought about throwing kicks to kind of intimidate him and see what he was going to do. I caught him and just followed up with some elbows.
"I want to fight again as soon as I possibly can. I know there's a card in Australia and South Korea -- either of those would be great. I can't wait for the next one. Whatever [UFC president] Dana White and Joe Silva have planned for me, I'm ready. I'm ready for whatever comes next."
Northcutt fights out of Katy, Texas. He has finished all but one of his six professional fights in the first round. He made his professional debut less than one year ago, on Nov. 14.