Warren, the ACC's leading scorer, finished with 20 points in his first game back from an ankle injury.
The Wolfpack (13-7, 3-4) trailed by 11 with under 16 minutes to play before rallying for their second straight win.
Daniel Miller scored a career-high 21 points for Georgia Tech (11-9, 2-5).
The Yellow Jackets had one last chance after Ralston Turner missed two free throws with 2.5 seconds remaining.
Miller heaved his inbounds pass to Kameron Holsey and he flipped the ball to Chris Bolden -- whose 30-footer from the wing was on line but bounced off the back iron.
Turner finished with 12 points, Desmond Lee had 11 and Tyler Lewis scored all 10 of his in the second half for N.C. State.
Trae Golden finished with 18 points for Tech. The Yellow Jackets had the ball in the final minute of OT with the score tied at 78 but N.C. State's Jordan Vandenberg stole Kameron Holsey's overthrown pass into the post with about 35 seconds left.
The Wolfpack called a timeout with 30.6 seconds remaining and milked most of the clock before Warren cut across the lane and knocked down a jumper over two Georgia Tech defenders.
The Yellow Jackets then hurried downcourt but Lee drew a charging foul on Golden with 2.5 seconds left. Turner was then fouled on the inbounds pass for N.C. State.
Quinton Stephens scored a career-high 13 points and Marcus Georges-Hunt added 13 more for Georgia Tech, which could've won it in regulation.
Lee tied it at 72 for N.C. State when he put back Warren's missed drive with 22.5 seconds left. The Yellow Jackets called a timeout with 16.1 seconds left to set their offense but Golden's kickout 3 with about a second left failed to draw iron.
Miller surpassed his previous high of 20 points, set two months ago against Dayton, for Georgia Tech. His jumper from the elbow with just under 16 minutes left made it 52-41.
But behind consecutive 3-pointers about 40 seconds apart by Lewis, the Wolfpack clawed back in it.
Lewis later knocked down a jumper in traffic with 9 minutes left to pull the Wolfpack to 57-56, and Desmond Lee's up-and-under layup 2 minutes later gave N.C. State its first lead since midway through the first half at 62-61.