David Noel finished with 10 points and 11 rebounds as the Tar Heels (22-6) won their eighth straight in workmanlike fashion.
Still, it was enough to earn a spot in the semifinals against the winner of the Maryland-Boston College game. Wes Miller made three 3-pointers and had 15 points for the Tar Heels.
Point guard Sean Singletary had 29 points and 10 rebounds for his first career double-double for Virginia (15-14), which can only hope for an NIT bid. J.R. Reynolds converted all but two of his 14 free throws to score 20 points despite shooting 3-for-16 from the field.
The Tar Heels missed seven shots in a row during one stretch of the early going and trailed 14-4 after about 5 1/2 minutes. They responded a 20-2 run to take control, with the final points coming courtesy of a technical on Cavaliers coach Dave Leitao.
Oddly, his anger came after a missed shot by North Carolina's Danny Green. Referee Bryan Kersey called the technical that led to two free throws from Miller, while Leitao still yelled on the sideline. Assistant coach Rob Lanier got off the bench to stand between his boss and the court, but Leitao wasn't finished.
He disgustedly tossed a rubber band on the court when Virginia eventually got possession, and during a media timeout moments later, he glared at Kersey for several seconds before returning to his team's huddle.
Perhaps it inspired the Cavaliers. They came back to force the final tie of the game at 24 on two free throws from Reynolds and trailed 39-34 at halftime.
North Carolina scored the first six points of the second half for an 11-point lead, and even though Virginia eventually got within four, the outcome never really was in doubt. Terry, Miller and Hansbrough made sure of it.
Terry narrowly missed his career high of 25 points scored earlier this season at Kentucky, and Miller reached double figures for only the second time in the past eight games. Hansbrough kept doing what he's been doing through all 28 games of his first season.
Earlier this week, he became the first freshman to be an unanimous selection to the All-ACC first-team, and he did nothing to disappoint in his first outing since the honor. Hansbrough now has scored at least 14 points in each game except one as he tries to become the first first-year player to lead North Carolina in scoring and rebounding.