The surprising Cavaliers (3-1, 3-0 Atlantic Coast Conference) also got 138 rushing yards from Cedric Peerman and several big plays from defensive end Chris Long as they won their third straight against ACC Coastal Division opponents.
Long batted several passes away, one turning into a 25-yard interception return, and sacked Taylor Bennett on fourth down at Virginia's 30 late in the game.
The Yellow Jackets got one more chance after a punt by Virginia set them up at their own 35 with 1:51 left, but two holding penalties moved them back and four consecutive incomplete passes by Taylor Bennett finished off the Cavaliers' victory.
Georgia Tech (2-2, 0-2) lost its second in a row and for the eighth consecutive time at Scott Stadium. Its last victory here came against No. 1 Virginia in 1990.
Sewell, whose shaky play against Wyoming helped prompt the coaching staff to get freshman Peter Lalich some turns at quarterback, played possibly his best game, and made the biggest throw of the day in the biggest spot to get Virginia back in front.
He finished 16-for-25 for 177 yards and the winning TD pass.
The Cavaliers led 21-7 after 13 minutes, but helped Georgia Tech get back in it, committing two turnovers that led to field goals and another mistake when Lalich's deep pass for Chris Gorham was intercepted by Morgan Burnett at the goal line.
That came right after Travis Bell's career-best 51-yard field goal gave Georgia Tech a 23-21 lead. But when the teams exchanged punts, Virginia made a huge play.
As Tech's Andrew Smith settled under Ryan Weigand's punt, Aaron Clark was bearing down on him and Smith muffed the catch, Trey Womack recovering for Virginia at the Yellow Jackets 26. On the next play, Sewell hit Jobe for the go-ahead touchdown.
On a day filled with costly mistakes, Smith's was the biggest.
Vic Hall muffed a punt at his own 30 early in the second quarter and Tony Clark recovered for the Yellow Jackets. Two runs by Jonathan Dwyer -- the second a 21-yarder off the left side -- pulled the visitors within 21-14 12:27 before halftime.
They got closer still on Travis Bell's 30-yard field goal five seconds before halftime, capping a 65-yard, 10-play march that Virginia's defense made look easy.
The Yellow Jackets had four plays in the drive covering 10 yards or more.
On the fourth play of the second half, Sewell was stripped of the ball by Darrell Robertson on an option play, and Vance Walker recovered for Tech at Virginia's 49.
Five plays later, Bell's 43-yard field goal made it 21-20.
Virginia led 21-17 at halftime, and at one point seemed primed for a blowout.
The Cavaliers drove 94 yards in 14 plays to take a 14-7 lead on Sewell's 4-yard run, then scored again 25 seconds later when Chris Long tipped a pass at the line and it fell in the arms of Jeffrey Fitzgerald, who cradled it for 25 yards and the touchdown.
It also was the first turnover of the season by Georgia Tech.