Rion Brown's 20 points led Miami (11-12, 2-8), which dropped to 0-6 in conference home games.
Miami's Raphael Akpejiori had a chance to tie the game at the free-throw line with 3.5 seconds left. He had grabbed an offensive rebound following a miss by Manu Lecomte, who scored 13 points.
Akpejiori, who was 4 for 4 from the line this season, made the first and missed the second.
The rebound was corralled by Kyle Washington, who missed both free throws and Brown's three-quarter heave was well short.
NC State shot 37.8 percent from the field (17 for 45) including 7 for 20 from behind the 3-point arc and sank 15 of 20 from the free-throw line. Miami, which came into the game shooting under 40 percent from the floor, shot 33.3 percent (17 for 51) for the game and 28.6 percent (8 for 28) in the second half.
NC State led 32-26 at halftime and scored three quick buckets in a 100-second span in the second to give the Wolfpack their largest lead of the game at 41-32.
But Miami battled back and tied the game at 51 with 1:37 left on a pair of free throws by Brown.
Moments later Warren countered with a pair of free throws for a 53-51 NC State lead.
Lecomte split a pair of free throws for Miami and Warren hit two to push the lead to 55-52. A 3-pointer was missed by Brown and Lecomte threw the ball away only to recover it after a bad pass by NC State's Desmond Lee, which bounced right to a wide-open Lecomte for a layup to pull within 55-54.
Turner made 1 of 2 from the line with 9.7 seconds leaving Miami with a chance to tie the game before Lecomte missed a layup and Akpejiori was unable to sink both free throws giving N.C. State the win.