Quinton Stephens missed two free throws with 4.7 seconds remaining that would've given Georgia Tech a four-point lead, but Cody Martin grabbed a defensive rebound and passed up court to a racing Lacey, who stopped short of 3-point line to hit the winner.
Marcus Georges-Hunt scored 23 points, Charles Mitchell had 18 points and Travis Jorgenson 14 for Georgia Tech (10-11, 1-8).
The Yellow Jackets led by four with 19 seconds remaining, but Lacey hit a layup to make it 80-78 and then closed with flurry.
Georgia Tech, which was coming off a surprisingly easy 20-point win at Miami, trailed by 14 points five times in the first half, taking their first lead when Georges-Hunt's three-point play made it 51-49 with 10:35 left in regulation.
In the closing seconds of regulation, Georges-Hunt had two chances to win it but missed a runner with 4.7 seconds remaining and was called for charging.
Lacey's desperation 3 from just inside the half-court line bounced off the rim as the buzzer sounded.
The Wolfpack were outrebounded 49-31, but they had just eight turnovers and finished with five more assists than the Jackets.
Georgia Tech closed within six in the first half after Demarco Cox hit a pair of free throws at the 2:17 mark.
Barber's straightaway 3 at the halftime buzzer put N.C. State up 40-31.