CHAPEL HILL, N.C. (AP) -- Texas coach Rick Barnes had told his players they would have to do something unexpected if they wanted to get more respect. The Longhorns figured out a way to do that Wednesday night with yet another win over North Carolina.
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.
''I said we're not going to be taken serious until we do something that we're not supposed to do,'' Barnes said. ''I said you've got a chance this week and it starts here. We prepared. ... We're tough. We've got a tough group of guys.''
Texas was the aggressor from the start, building a double-digit lead and staying in control nearly all game. And when the Tar Heels made their late push, Holland's stickback offered the perfect example of how this season's group can overcome its mistakes.
With his team protecting an 84-83 lead, Holland missed his first free throw with 7.2 seconds left and knew his second was short as soon as it left his hand. He raced inside and grabbed the rebound in a crowd, then put up a shot that bounced around the rim before dropping through the net.
Paige got a good look on the final possession from in front of the UNC bench, but the shot rimmed out at the horn to seal Texas' fourth win by three or fewer points.
''We've been grinding out games all year and we've been finishing late,'' Holland said. ''... We've had a lot of preparation leading up to his game with situations like that. It just shows how tough we are and how together we are and how we're still growing, how we can just stick together as a team in the end.''
Barnes suffered through a miserable 16-18 record last season, ending with a first-round loss in the CBI. But the Longhorns entered this one with five players averaging in double figures and continued their balanced-scoring ways.
Isaiah Taylor scored 16 points to lead Texas, while Jonathan Holmes had 15 points and 10 rebounds. In addition, Javan Felix scored 12 points - including two key baskets in the final 2 minutes to answer a tying spurt from the Tar Heels despite going just 2 for 11 the rest of the game.
''He always tells us to have the confidence to take shots,'' Felix said of Barnes. ''That's what I did.''
Paige scored 23 points to lead UNC, while senior Leslie McDonald scored 15 with four 3-pointers in his first game after missing nine due to NCAA eligibility issues.
But in the end, the Tar Heels struggled to overcome a flat start as well as 23 missed free throws in what has become a recurring theme.
North Carolina, which had beaten highly ranked Michigan State, Kentucky and reigning national champion Louisville in the past month despite playing without McDonald and leading scorer P.J. Hairston due to those NCAA issues, trailed by 13 points and spent Wednesday fighting uphill in a performance that had coach Roy Williams seething.
''I am not happy, guys,'' Williams said. ''I am not in the daggum Christmas spirit. ... If you want to really know how ticked off I am, I told them we would practice at midnight tonight. And then I told them I better check the NCAA rules so we cannot practice at midnight tonight.
''We cannot practice until 5 a.m. And everybody's (butt) will be in here at 5 a.m. this morning.''
McDonald's return came after the NCAA announced hours before tipoff that the senior was cleared. The NCAA said McDonald must repay $1,783 to a charity of his choice for receiving improper benefits from ''numerous individuals'' during this spring and summer.
After the game, UNC athletic director Bubba Cunningham said in a statement the school was still working with the NCAA on Hairston's status and expected to have the matter resolved by the end of the week.
UNC lost starting center Joel James to a right knee injury on the game's first play. The extent of his injury is unclear.
Follow Aaron Beard on Twitter at https://www.twitter.com/aaronbeardap