Georgia Tech's hopes for an upset were dealt a major blow in the first half when quarterback Josh Nesbitt injured his right forearm attempting to tackle Davon Morgan after Morgan had intercepted a Nesbitt pass.
Nesbitt had two scoring runs in the first period, one of them a 71-yarder, before suffering the injury.
Georgia Tech, with Tevin Washington filling in for Nesbitt, still held a 14-7 lead heading into the fourth quarter, but Wilson tied it on a 15-yard run with 13:21 to play and Andre Smith caught a 2-yard pass from Tyrod Taylor with 6:34 remaining to put the Hokies in front.
Washington then drove Georgia Tech 80 yards in nine plays and the Yellow Jackets moved back into a tie with 2:34 left on Orwin Smith's 9-yard run.
Wilson, however, went the distance with the ensuing kickoff.
Georgia Tech marched to the Virginia Tech 16-yard line after Wilson's score, but with 8 seconds left Washington was intercepted in the end zone by Rashad Carmichael.
Virginia Tech improved to 7-2 for the season and is 5-0 in the Coastal Division of the Atlantic Coast Conference. The Hokies have a two-game lead in the division with three to play.
Georgia Tech fell to 5-4 and 3-3.