The Longhorns needed Joseph's 20th and 21st points in large part because of Carolina freshman Harrison Barnes, who showed some heroics of his own. Barnes hit a game-tying three-pointer with 12.7 seconds left, setting up Joseph's attempt. Joseph drove to the top of the key, then faked Strickland into the air. He then turned and sank the game-winner.
The shot helped complete a comeback for the Longhorns, who trailed most of the second half.
North Carolina (7-4) led by one, 33-32 at halftime, thanks largely to a defensive effort that held Texas to 35.3 percent shooting from the field. The Tar Heels weren't much better in the first half, shooting just 37.5 percent themselves.
But both offenses were on-track in the second half. Texas shot 18-34 (52.9 percent), while North Carolina made 17-34 shots (50).
While Joseph set a career-high with 21 points on 8-14 shooting, Jordan Hamilton returned to his old scoring self, putting in 24 points of his own by shooting 10-18, and 4-7 from three-point range. He also led all rebounders with 10. Gary Johnson added 11 points and J'Covan Brown scored 10.
But in the end, it came down to one shot. And as he did against Illinois — or as he didn't do against Pittsburgh — Joseph made it.
The win for No. 22 Texas (9-2) was a big one, setting the Longhorns up well for the remaining difficult stretch of non-conference games. Next, the Longhorns will travel to play No. 14 Michigan State, and Texas still has a showdown with No. 4 Connecticut in Austin on the horizon.