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Hansbrough was 5-for-11 from the floor and 14-for-15 from the free throw line to lead UNC (17-2, 4-1 ACC) in scoring for the 13th time this season.
Brandan Wright's streak of 18 consecutive games in double figures was snapped. He finished with nine points on 3-of-6 shooting.
The Yellow Jackets (13-5, 2-3) fought back from an early nine-point deficit to pull within two at 15-13 midway through the first half. However Carolina outscored them 16-7 after that, before both teams suffered through 4:36 field goal drought prior to halftime.
"I definitely feel like we got at them early," Terry said. "We got some offense going and got some shots on the floor and that stopped them on the defensive end and things started going our way."
The Tar Heels hit five of its eight three-point attempts in the first 20 minutes as they took a 34-23 advantage at the break.
"We should have had an even better working margin than the 11 points," Williams said. "At the end of the first half we had four turnovers out of the last six possessions and two of them were on a break."
Crowd favorite Quentin Thomas played 13 error-free minutes with two assists, two rebounds, a block and a steal without a turnover.
"North Carolina just outplayed us tonight," Tech coach Paul Hewitt said. "They were much more physical than we were, and from the opening tip they just took it to us the whole night."
For the sixth time this season, Carolina forced its opponent into 20 or more turnovers. Tech's 21 turnovers led to 20 points for the Tar Heels.
"That is the key to our success is of our defense," said Danny Green, who scored five points and gathered four rebounds in 15 minutes. "We're holding teams shooting to 40 percent, and we make them turn it over, and that's how we get easy baskets."
The Tar Heels travel to Winston-Salem to take on Wake Forest Wednesday at 7 p.m.