Gurley's 25-yard touchdown run in the second and final overtime gave Georgia its first lead.
Georgia Tech (7-5) blew leads of 20-0 in the second quarter and 20-7 at halftime.
Lee threw two touchdown passes to DeAndre Smelter as Georgia Tech, which usually emphasizes the run in its spread-option offense, instead attacked Georgia through the air.
Mason completed 22 of 36 passes for 299 yards with two touchdowns and one interception.
Georgia won the toss to start overtime and chose to play defense. Smelter ran for 12 yards on a reverse to help set up Lee's scoring run from the 2.
Georgia answered with a strong dose of Todd Gurley on its first overtime possession. Gurley had gains of 8, 11 and 6 yards on the Bulldogs' quick three-play touchdown drive.
Georgia Tech then elected to play defense in the second extra period. Gurley ran straight through the Georgia Tech defense for a 25-yard touchdown run and the Bulldogs' first lead at 41-34.
Georgia Tech's Robert Godhigh was tackled by Leonard Floyd for a loss of three yards to set up a fourth and 5 from the 6. Wilson tipped Lee's pass for Darren Waller before cornerback Damian Swann batted the ball out of the end zone for the incompletion to end the game.
Georgia players then rushed the field, their dominance in the state rivalry still intact.
Georgia Tech did not have a turnover until Lee, throwing off his back foot, had his pass intercepted by Josh Harvey-Clemons in the fourth quarter. Clemons returned the ball 18 yards to the Yellow Jackets 25.
Jeremiah Attaochu's fourth sack of the game helped force Georgia to settle for Marshall Morgan's 32-yard field goal for a 27-27 tie with 4:17 remaining.
The Yellow Jackets took a 20-0 lead before Georgia scored 17 unanswered points to cut the lead to three points. Lee's 7-yard scoring pass to Smelter in the fourth quarter pushed the lead back to 10 points.
Gurley's 2-yard touchdown run with 6:37 remaining again trimmed Georgia Tech lead to three points at 27-24.
Mason struggled through most of the first half and appeared tentative in some of his passing decisions.
Of Georgia's 152 yards in the half, 86 yards came as Mason looked more comfortable running the 2-minute offense in the Bulldogs' final drive. Mason completed each of his five passes on the drive, including back-to-back completions of 17 and 22 yards to Chris Conley.
Gurley scored on a 9-yard pass, taking off from about the 4-yard line and soaring with his body out of bounds but the ball stretched out over the corner at the goal line.
Georgia Tech dominated most of the half. A big pass from Lee to Waller on the Yellow Jackets' opening possession set the pace for the half. On third and 8 from the 26, Lee's lofted a deep pass to Waller, who caught the ball in stride behind the coverage of cornerback Sheldon Dawson for a 68-yard gain to the Georgia 6. Lee scored on a keeper from the 3.
The Yellow Jackets used another big pass play on their next possession, a 43-yarder from Lee to running back Robert Godhigh, to set up Harrison Butker's 37-yard field goal.
Mason, under pressure, threw a weak attempt for Conley late in the opening quarter that was intercepted by Jemea Thomas at the Georgia 36. Lee's 26-yard pass to Smelter gave Georgia Tech a 17-0 lead. Butker's 22-yard field goal in the second quarter pushed the lead to 20-0.
Georgia's lost senior defensive end Garrison Smith to a left ankle injury in the third quarter. Smith did not return.