AUSTIN, Tx. — Texas entered its game against North Carolina here on Wednesday night with one of the worst-performing offenses in major college basketball. The Longhorns ranked near the bottom nationally in both points per possession and points per game.

Perhaps facing the Tar Heels’ struggling defense is just what Texas needed to break out of a season-long offensive funk. During their 85-67 victory, the Longhorns led by as many as 19 in the first half and continuously rebuffed the Tar Heels’ attempts to rally in the second half.

“It was an ugly night for us, to say the least,” said UNC coach Roy Williams, who described his team’s play as “timid.”

Like the Heels’ two defeats before Wednesday night, this one was marked by long stretches of defensive futility, an inability to make shots on offense and well-intentioned second-half rally that simply wasn’t good enough. Try as they might to climb out of hole they had a hand in digging, the No. 23 Tar Heels (8-3) couldn’t – not after an abysmal first half.

The Longhorns’ 46 first-half points were their most in a first half this season, and tied for their most in a half overall. They shot just 41.3 percent during the first half but built such a large lead thanks in large part to the fact that they attempted 16 more shots from the field than UNC.

Though the Longhorns (7-4) are prone to turnovers, UNC forced them to commit just four of those during the first half. The Tar Heels had eight, and Texas turned them into 10 points. Even more damaging for UNC were Texas’ 14 second-chance points during the half.

The Longhorns during the first 20 minutes had more offensive rebounds (12) than defensive (11). Offensive rebounding was a major point of emphasis for UNC coach Roy Williams, who was infuriated on Saturday when his four post players finished without a single offensive rebound.

The Heels fared better on Wednesday, but missed enough close shots to last a few games, let a single one. UNC shot just 31.3 percent. Texas wasn’t all that much better at 40.5 percent, but the Longhorns took 74 shots from the field – nearly 20 more than their average.

“I told the players when we came in,” said UNC junior guard Reggie Bullock, who led the Heels with 18 points. “We can’t keep playing like this. If we keep playing like this, teams are going to keep kicking our [butt].”

If Williams and his team could take solace in anything, it’s that it didn’t go away easily. Three times during the second half, UNC cut the Texas lead to six point. Twice, the Heels cut the Longhorns lead to four, and there were times when it seemed UNC might have enough to muster a memorable comeback.

Williams, in fact, said he believed his team would have a chance in the end. Each time UNC came a little closer, though, the Longhorns stretched their lead back out.

“It was like a comedy of errors, except it wasn’t very blanket-blank funny,” Williams said. “But we still kept trying, kept trying.”

After Bullock made a difficult shot in the lane to cut Texas’ lead to 60-56, the Longhorns’ Julien Lewis scored five quick points – three of them on a long 3-pointer from the left baseline that put Texas back ahead by 10, 68-58, with less than five minutes to play.

The Tar Heels never seriously threatened again.

Sheldon McClellan led Texas with 17 points and Jonathan Holmes, who scored eight consecutive points at one point in the first half, finished with 15 points. Lewis finished with 16.

James Michael McAdoo, the sophomore forward, added 14 points for the Heels. McAdoo and Bullock were the only players who scored in double figures for UNC. And Bullock was the one of the few whom Williams singled out in a positive way after the game.

Williams said his players needed to better buy into what he and the coaching staff are teaching. McAdoo agreed.

“I mean, we buy in – we beat this team easily,” he said.

The defeat was a humbling one for UNC, which entered winter break hoping to resolve some of the problems – defensive lapses, offensive inefficiency, lack of rebounding – that have hounded the team since the beginning of the season.

But instead of coming closer to finding solutions, UNC suffered a defeat that perhaps raised more questions about which direction the Heels are headed. During the final minute, a sparse crowd of students inside the Erwin Center serenaded the Heels with a brief chant of “over-rated.”

When the weekly top 25 polls come out on Monday, it’s likely the Heels won’t be rated at all.

Carter: 919-829-8944 Twitter: @_andrewcarter