GREENSBORO, N.C. (AP) - Freshman Cory Joseph hit a turnaround jumper over Dexter Strickland with 1.4 seconds left to help No. 22 Texas beat North Carolina 78-76 on Saturday.

Joseph had a season-high 21 points for the Longhorns (9-2), while Jordan Hamilton had a team-high 24 points as Texas trailed for most of the second half before rallying in the final 3 minutes to edge out the Tar Heels (7-4) playing in front of an instate crowd.

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Strickland matched his career-high with 18 points for North Carolina. Freshman Harrison Barnes added 16 points, including the tying 3 with 12.7 seconds left that set up Joseph's winner.

Joseph drove to the top of the key against Strickland and pump-faked to get the sophomore airborne, then spun to his right and lofted a shot that dropped cleanly through the net for the lead.

The shot sent the Texas bench into celebration, though the Tar Heels had a chance to answer. They inbounded the ball to halfcourt and called a timeout to set up a play with 0.8 seconds left, but Kendall Marshall managed only a desperation 3 that hit all backboard as the horn sounded.

Hamilton went 10 for 18 from the field and made four 3-pointers to go with 10 rebounds to lead the Longhorns.

Tyler Zeller, the team's leading scorer, managed 14 points for the Tar Heels.

It was a good win for the Longhorns as they enter a tough stretch of nonconference games. Next up is a trip to No. 14 Michigan State on Wednesday followed by a home game against No. 4 Connecticut three games later before opening Big 12 Conference play against Texas Tech.

As for the Tar Heels, they fell just short in adding another marquee victory to their resume. They edged Kentucky two weeks ago at home, but had played just two games since during exams and couldn't quite pull this one out when things got tight late.

Texas led by 10 points in the first half before North Carolina finally stood up to the Longhorns' physical play inside and kept them off the offensive boards. North Carolina rallied to take a 33-32 halftime lead, then led by as many as seven points three times to charge up the arena located about an hour west of the Chapel Hill campus.

Tristan Thompson's dunk over Zeller gave Texas a 74-73 lead with 45.4 seconds to play. Then, after Zeller missed a hook shot on a good look with about 30 seconds left, J'Covan Brown hit two free throws to push the margin to three.

Barnes answered with a confident catch-and-shoot 3 over Dogus Balbay from the left wing to tie it, only to see Joseph top him on the next possession.

Hamilton went 10 for 18 from the field and made four 3-pointers to go with 10 rebounds to lead the Longhorns.

Zeller, the team's leading scorer, managed 14 points for the Tar Heels.