Reyshawn Terry proved to be a match-up problem for UVa, as he scored 24 points on 8-of-13 shooting. Terry was spectacular on drives to the hoop, bursting out of an 8-for-29 field goal slump over the previous three games.
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"I'm just happy we won," Terry said. "We understand that every game is not going to be pretty. We just have to be willing to take the challenge when it comes."
Tyler Hansbrough was hounded by double and triple teams most of the night, but finished with 17 points anyway.
Wes Miller didn't miss a shot en route to a 15-point performance, while David Noel registered a double-double with 10 points and 11 rebounds. It was just the second time in eight games Miller reached double figures.
"As a kid I would come to ACC Tournament and it's like a dream come true to actually play here," Miller said. "I had to pinch myself to make sure I wasn't dreaming."
With Bobby Frasor in foul trouble, rapidly improving Quentin Thomas got in for 24 minutes, dishing out six assists and picking up a couple of steals against two turnovers.
Thomas, whom Williams simply refused to give up on earlier in this season, now has 39 assists and 10 turnovers in his last 12 games.
Despite missing nine of its first 10 shots and falling behind 12-2, Carolina recovered and went on a 22-4 run from that point before settling for a 39-34 halftime lead.
Miller was a perfect 3-for-3 from three-point range – successfully shaking off his quiet shooting night last Saturday at Duke.
"I just think that we came out a little flat, but you've got to give Virginia a lot of credit, because they really came at us tonight," Miller said. "They got all of our guards in foul trouble, and we didn't do some of the things that we work on in practice and that Coach tells us to do.
"But it's always important to win basketball games, especially this time during the year. We're just happy we were able to gut that one out and keep moving on."
First-team all-conference guard Sean Singletary scored 17 of his game-high 29 points in the first half.
Virginia fell to 15-14.
"It really doesn't matter what type of game that we had. We lost. Our season is over," said Singletary.
Carolina (22-6) finished shooting 57 percent, while out-rebounding the Cavs, 43-36.
UNC will face No. 11 Boston College (25-6) on Saturday at approximately 4 p.m. The Eagles easily dismissed Maryland, 80-66, in the nightcap on Friday. Back on Jan. 25, BC defeated the Tar Heels in Chapel Hill, 81-74.