Sheldon McClellan scored 18 points with six rebounds and Julien Lewis added 16 points, as Texas jumped out early, staved off an early second-half rally then rolled to the finish line past No. 23 North Carolina, 85-67.
Jonathan Holmes made 6-of-9 shots for 15 points to go along with eight rebounds and Ioannis Papapetrou donated 10 points for Texas (7-4), which has won two straight.
"It was a great team win. I'm happy for these guys because tonight they started seeing some of the things we had talked about," Texas coach Rick Barnes said. "We haven't faced that defensive pressure all year. It's the hardest pressure we've faced."
Reggie Bullock led North Carolina (8-3) with 18 points, while James Michael McAdoo added 14 points, nine rebounds and six steals. The Tar Heels saw their three-game winning streak come to an end.
Texas scored the first six points in a precursor of a dominate first half that saw the advantage grow to as many as 19. Connor Lammert's high-arching 3- pointer made the score 11-2 and Lewis' triple moments later gave the Longhorns their first double-digit lead, 14-4.
The Longhorns stayed comfortably in front with Lewis' layup and 3-pointer opening the largest edge at 39-20. UNC head coach Roy Williams decided to let his team play through the slide and it responded, cutting the margin to 46-33 at the half.
North Carolina came out much more aggressive in the second 20 minutes, as McAdoo asserted himself into the offense and Bullock started to get going as well. His 3-pointer cut the deficit to 48-39, and McAdoo's steal and slam moments later brought the visitors within 52-46.
Freshman Marcus Paige connected on a floater in the lane to make the score 54-50, but that's as close as the Tar Heels got. Demarcus Holland's three- point play upped the lead to seven. The margin grew to 10 and then was cut again to four at 60-56 thanks to Bullock's mid-range jumper.
However, the Tar Heels again hit the wall, as Texas responded and went back in front by double digits at 68-58 on Lewis' 3-pointer with just under five minutes to play.
The Tar Heels kept missing from the perimeter and the Longhorns made their free throws down the stretch to capture the victory.
"It was an ugly night for us to say the least," North Carolina coach Roy Williams said. "They out ran us. We like to say that we are a running team but Texas did a better job tonight of pushing the pace, and getting us back on our heels."
Texas made 40.5 percent of its shots, while the Tar Heels managed to connect on only 31.3 percent of their attempts, including a 3-of-19 mark from beyond the arc ... Dexter Strickland scored nine and Paige added seven for the Tar Heels ... Cameron Ridley posted eight points and six rebounds, while Javan Felix donated eight points and eight assists for Texas ... Texas leads the all-time series, 5-3.