Olivier Hanlan paced Boston College (9-13, 1-9) with a season-high 30 points, and Aaron Brown scored 18 with six boards.
Playing in front of a near-capacity crowd that was half-filled with fans wearing Carolina blue, the Tar Heels took control with a 13-3 run midway into the second half.
Hicks had a pair of baskets and the team's leading scorer, Marcus Paige, capped it with his first basket of the game, a 3-pointer from the left wing that made it 58-45 with 11½ minutes to play.
The teams were tied at halftime and BC took a 38-36 edge on Brown's basket in the lane before the Tar Heels scored the next six points.
After the Eagles cut it to 45-42 on Dimitri Batten's driving shot, North Carolina went on its key run.
BC closed it to five points three times in the closing five minutes, but North Carolina hit a few baskets to stay in control.
Coming off consecutive losses to ranked teams (then-No. 10 Louisville and No. 3 Virginia), the Tar Heels played sloppily in a foul-filled opening half that didn't generate much of a flow. North Carolina had two possessions in the opening three minutes when it threw passes into the backcourt for violations.
The teams were whistled for 11 fouls apiece and combined for 15 turnovers (North Carolina had 10) and went to the locker room tied at 36 at halftime.
North Carolina: The Tar Heels pounded the ball inside much of the game, especially when BC's 7-footer Dennis Clifford went to the bench with early foul trouble. They hit 20 of 27 free throw attempts.
Boston College: F Will Magarity, a 6-foot-11 forward who spells Clifford, missed his second straight game with to a concussion. He'll likely return for the next game.
North Carolina: At Pittsburgh next Saturday.