Erik Swoope added a career-high 14 points for the Hurricanes (9-6, 1-2 ACC), who took control late in the first half and led by 13 points after the break against the cold-shooting Tar Heels (10-5, 0-2).
Miami was coming off a tough 49-44 loss at No. 2 Syracuse over the weekend and had lost three overtime games this season. Coach Jim Larranaga is hoping his group is figuring out how to be successful with an overhauled roster, including with the use of a zone that clamped down on UNC's inside game and left coach Roy Williams lamenting his team's lack of offensive movement.
The suddenly reeling Tar Heels, who were coming off a 73-67 loss at Wake Forest in one of their worst performances of the season, shot just 31 percent (20-for-65) and finished with a season-low scoring output.
Brown went 7-for-14 from the floor with two 3-pointers to handle the bulk of the offense for Miami, which shot 42 percent while being patient and making the Tar Heels repeatedly defend deep into the shot clock.
Brown also got a cut under his left eye when he was hit by an elbow from UNC starting center Joel James during a scramble for the rebound early in the second half, leading to James' ejection for a flagrant-2 foul with 18:31 left.
The Tar Heels looked ready for a bounceback performance from the Wake Forest loss when they jumped to an 8-0 lead in the first two minutes, only to find out that was about as easy as things would get for the entire game.
Now the team that has beaten highly ranked Michigan State, Kentucky and Louisville this season has five losses to unranked opponents. Things won't get any easier Saturday with a trip to No. 2 Syracuse.
James Michael McAdoo scored 12 points for North Carolina, but leading scorer Marcus Paige struggled for the second straight game. After finishing with a season-low eight points against Wake Forest, he scored eight again on 2-for-15 shooting against Miami.
Garrius Adams hit a 3-pointer just before the horn to give Miami a 29-23 halftime lead. Then, after the Tar Heels clawed to within a single basket with 14½ minutes left, Miami answered with four straight scoring possessions.
That run ended with back-to-back dunks from Swoope that gave Miami a 10-point lead, which would ultimately reach 46-33 on Adams' layup at the 9:59 mark.
The Tar Heels got no closer than four again, with J.P. Tokoto missing a 3-pointer with about 15 seconds left and the Tar Heels down five in what amounted to their last gasp.
James finished with four points and five rebounds before his ejection. He had missed four straight games with a knee injury.