Ralston Turner added 22 points for the seventh-seeded Wolfpack (20-12), who will challenge second-seed Syracuse in the next round.
Rion Brown netted 22 points to pace the 10th-seeded Hurricanes (17-16).
NC State opened the game on a 10-2 run, but Miami responded with a 10-3 run of its own to keep things close midway through the first half. The Wolfpack would lead by no more than five points the rest of the period, entering the break with a 26-22 advantage.
The two teams continued to trade runs after intermission. First, following a jumper from Brown, NC State rattled off six straight points to take a 32-24 lead.
Just over three minutes later the Hurricanes pulled ahead, 33-32, with a quick 9-0 spurt. In response, the Wolfpack used a 10-2 run to take a seven-point lead.
They were also up seven with 6:41 to play, when Miami scored nine straight, capped by a 3-pointer from Davon Reed, putting it ahead 53-51.
However, the Hurricanes' advantage was short-lived, as Turner hit a pair of free-throws, after the teams traded turnovers, to start a decisive 12-0 run.
NC State' 26-7 scoring edge off of turnovers was a major factor in the decision.