Demarcus Holland scored on a stickback of his own free throw with 4.1 seconds left to help Texas hold on and beat the 14th-ranked Tar Heels 86-83, its sixth straight win.
Holland finished with 15 points for the Longhorns (10-1), who survived a missed 3-pointer from UNC's Marcus Paige on the final play.
Texas shot 38 percent after halftime and 40 percent for the game, but dominated the boards and scored 21 second-chance points to beat the Tar Heels (7-3) for the sixth time in seven meetings.