Aaron Murray threw four touchdown passes, including a 25-yarder to Justin Scott-Wesley with 1:47 remaining.
The Bulldogs (3-1, 2-0 SEC) completed their opening-month run through a gauntlet of top 10 teams with a victory that propelled them back into the thick of the national championship race.
LSU (4-1, 1-1) got a career-best 372 yards passing from former Georgia quarterback Zach Mettenberger in his return to Athens, and the Tigers went ahead 41-37 on Jeremy Hill's 8-yard touchdown run with 4:14 to go.
But that was plenty of time for Murray and the high-powered Bulldogs on a day when neither defense had much success. He completed three straight passes to quickly move the Bulldogs into LSU territory, and freshman J.J. Green broke off an 18-yard run to the Tigers 25. Then it was Scott-Wesley, breaking wide open behind the secondary to haul in a pass and tiptoe just inside the pylon for the winning score.
Murray ran for Georgia's other touchdown on a sneak and finished with 298 yards passing in Georgia's second victory over a top 10 team after a season-opening loss to Clemson.
Two out of three against top 10 opponents? Georgia will take it.
About 10 minutes after the game, dozens of Georgia players ran back on the field to celebrate with their fans along the famed hedges at Sanford Stadium.
Murray and Mettenberger were in the same recruiting class at Georgia, contending for the starting job in the spring of 2010 until a criminal case ended the competition.
Mettenberger pleaded guilty to misdemeanor sexual battery charges and was kicked off the team that summer. His mother, Tammy, still works in football operations for the Bulldogs, though coach Mark Richt gave her the week off because of all the attention surrounding her son.
The former teammates did all that could be expected of them.
Mettenberger had three touchdowns on 23-of-37 passing, continually burning the Bulldogs on third down. He completed a 25-yard pass on Odell Beckham on third-and-22 to improbably extend an LSU drive that led to Hill's go-ahead touchdown.
But Murray delivered the final blow.
Georgia did plenty of damage on the ground in the first half, but star running back Todd Gurley sustained an apparent left ankle injury on a 25-yard run. He didn't return, watching the second half while wearing a windbreaker and walking boot.
The Bulldogs weren't nearly as effective on the ground with Keith Marshall handling the load, but Murray and his receivers took up the slack. Chris Conley had five catches for 112 yards and a touchdown. Michael Bennett hauled in a pair of scoring passes.
Georgia finished with 494 yards, though the bulk of those came in a back-and-forth first half that ended with Georgia on top 24-17.
Little-used Kadron Boone had two early touchdown catches for LSU, but Jarvis Landry turned out to be Mettenberger's go-to receiver. The junior had 10 catches for 156 yards, including a 39-yard touchdown that tied the game at 27 late in the third quarter.
After facing Clemson, South Carolina and LSU, Georgia has a much easier schedule the rest of the way, with only one more ranked team in the regular season -- injury plagued Florida. That sets up the Bulldogs to make a run to their third straight SEC East title and trip to the conference championship game.
LSU has a much tougher road, with games still remaining against top-ranked Alabama and No. 10 Texas A&M.