The Tar Heels reached Saturday's semifinals to face seventh-seeded Maryland, which upset second-ranked Duke earlier Friday. UNC has reached the past two finals and is trying for its first title since 2008.
Michael Snaer scored 20 for sixth-seeded Florida State (18-15), which lost all three meetings with the Tar Heels this season with the last two coming by 21 points each.
Hairston, playing in his hometown, hit his first four 3-pointers and finished 7-for-11 from the field, including 5-for-6 from behind the arc. But he suffered a cut to the webbing between two fingers and left a trail of blood droplets as he checked out of the game. Hairston left the bench area in obvious pain with 4:13 left.
Hairston needed stitches for the cut, but the severity of his injury wasn't immediately known after the game.
The Seminoles advanced to the quarterfinals by holding off 11th-seeded Clemson in the first round Thursday night. But they struggled to slow Hairston early and then Bullock after halftime, as the Tar Heels' four-guard lineup returned to the form it displayed in a six-game winning streak before losing to Duke at home last weekend.
Two of Hairston's first-half 3s fueled an 8-0 burst that gave UNC a 10-point lead, then Bullock sparked the 13-0 second-half run that helped the Tar Heels blow the game open.
After FSU closed to within 39-35, Hairston started the run with a 3, while Bullock followed two possessions later with his own 3 over Devon Bookert. Bullock also had a driving layup while drawing a foul for a three-point play, then Hairston closed the run with two free throws to make it 52-35 with 14:15 left.
Florida State never managed to get that deficit back to single digits.
Bullock went 7-for-11 and scored 13 of his points after halftime. James Michael McAdoo added 12 points for UNC despite foul trouble, while Dexter Strickland added 10.
Snaer - the senior with six buzzer-beating winners in the past two seasons - fouled out with 1:40 left and headed to the bench to a standing ovation from his teammates. He finished 8-for-12 from the field and 3-for-5 from behind the arc to go with seven rebounds and five assists.