Miami, FL – Harrison Barnes had 23 points and six rebounds as 64 win over Miami-Florida.
Durand Scott had 15 points and Kenny Kadji added 13 points and seven rebounds for the Hurricanes, (15-9, 6-5), who have lost their last two.
Miami led by as many as nine points in the first half when Reggie Johnson put in a layup for a 31-22 advantage with under five minutes to play.
North Carolina, though, was able to cut that to five as Henson's layup made it a 35-30 game at the break.
A Scott jumper four minutes into the second half put the Hurricanes up by eight, 44-36, but Harrison Barnes countered with a three-pointer to kick off an 8-0 run that saw P.J. Hairston tie the game with a pair of free throws.
It remained tight for the next several minutes until Kendall Marshall put in a pair of free throws and North Carolina used that to start a 10-2 run. Bullock's three capped the burst and made it a 63-55 game with 6 1/2 minutes to play.
Rion Brown countered with a three, but the offense went cold over the next three minutes until James Michael McAdoo hit a free throw and Bullock buried a three with under two minutes to play for a 67-58 lead.
"In the second half we had our chances, but they outplayed us at the critical time of the game," said Miami head coach Jim Larranaga.
Miami never got closer than six points the rest of the way.
North Carolina hosts Clemson on Saturday...Miami-Florida hosts Wake Forest on Saturday...The Tar Heels have won 10 straight over the Hurricanes and 18 of 20 overall in the series.