Bullock scored the game's first eight points and outscored Maryland 21-20 through the opening 20 minutes, then set his career high with a straightaway 3-pointer with 5:45 left for his only second-half basket.
UNC shot 35.4 percent (23 of 65) for the game, including 23.5 percent (8 of 34) after halftime. But the Tar Heels scored 14 points off turnovers - all in the first half - and Maryland finished with 21 turnovers.
Dez Wells scored 21 points on 8-for-11 shooting to lead the Terrapins, while Alex Len had 10 points. But Maryland managed just five assists for the game and shot 39.6 percent (21 of 53), including 1 of 12 from 3-point range, for an ugly follow-up to Wednesday night's upset of North Carolina State on Len's last-second basket.
Bullock quickly turned the game into his own show. The 6-foot-7 junior buried a 3-pointer on the game's opening sequence, followed with a transition layup, then added another 3 on the next possession for a personal 8-0 run to start the game. Bullock kept hitting, knocking down another shot from behind the arc and six free throws, with the last three coming when he was fouled on a 3-point attempt.
While Bullock was rolling, the Terrapins were sputtering in ugly fashion.
Maryland had two assists with 15 turnovers in those opening 20 minutes, as North Carolina's defense played with an aggressive and active style it hasn't shown often this year. The Tar Heels repeatedly had their guards come down to slap at the ball when Len tried to move in the post, while the Terps' perimeter players kept throwing the ball away.
The Terrapins had just one shot attempt and five turnovers in the first three minutes, then gave the ball away at midcourt on their last possession of the half to give Dexter Strickland an uncontested dunk as the final seconds ticked away. That capped a 9-0 run that gave the Tar Heels a 42-20 lead at the break.
Maryland played better after halftime and UNC lacked its first-half intensity, helping the Terrapins shave some off the Tar Heels' lead, which reached 23 early in the second half. But the Terrapins couldn't manage a serious push and got no closer than the 10-point final margin.
North Carolina, which was coming off a win at Florida State last weekend, has won 11 of the last 15 in the series.