Neither team reached the end zone through the first three quarters, but the teams traded touchdowns back and forth over the final three minutes before the Tigers (5-0, 3-0 SEC) came out on top in their second straight close call.
With Georgia (3-2, 2-1 SEC) ahead 7-6 after finally scoring in the opening minute of the fourth period, LSU reclaimed the lead, 12-7, on Scott's 2-yard run with 2:53 remaining. The Bulldogs bounced back on Joe Cox's 16-yard touchdown pass to A.J. Green with 1:09 left, going up 13-12 before missing a 2-point conversion.
But LSU, starting in good field position after an unsportsmanlike conduct penalty on Georgia, was already in field goal range when Scott broke two tackles at the line and went all the way to the end zone.
Next week, LSU hosts top-ranked Florida.
No one could have expected such a finish after the teams settled into a defensive struggle, Georgia weathering a dominating performance by LSU in the first half to only trail 6-0.
Georgia dominated the third quarter, sparked by a hard-rushing defense that sacked Jordan Jefferson six times, and the hard running of freshman Washaun Ealey, who gained 33 yards on eight carries in his first college appearance.
Cox hooked up with Orson Charles on a 22-yard reception, and Georgia recovered even after Charles was dubiously flagged for unsportsmanlike conduct for pumping his right fist after making the big catch.
The Bulldogs got it to the 1 on a pass to Michael Moore, who came up just short of the goal line. On fourth-and-inches, Georgia decided to go. Cox faked a handoff to Caleb King, then spotted fullback Shaun Chapas, who made the touchdown catch while falling backward to give Georgia its first lead of the game.
But that catch was overshadowed by the ending.
Jefferson completed a 16-yard pass on third down to Rueben Randle, hit Scott on a screen for another 16 yards, and got loose down the sideline for a 27-yard run that set up Scott's first TD. LSU went for the 2-point conversion, but Jefferson was sacked again.
Trailing 12-7, Georgia quickly drove downfield. Tavarres King got loose behind the secondary and hauled in a 46-yard pass from Cox. One play later, the senior quarterback threw it for grabs in the end zone and Green reached over cornerback Chris Hawkins to snatch the ball before tumbling into Sanford Stadium's famous hedge.
But, with the crowd going nuts, Georgia was flagged again for excessive celebration. The Bulldogs missed their 2-point try, then had to kick off from their 15. Trindon Holliday returned it to the Georgia 43, and a 5-yard penalty for an illegal formation pushed LSU even closer.
Two plays later, Scott appeared stopped at the line by Rennie Curran and Marcus Dowtin. But the LSU runner stayed on his feet and didn't stop until he was in the end zone.
Scott rushed for 95 yards on 19 carries, while Jefferson was 18 of 27 for 212 yards. Cox completed 18 of 34 for 229 yards, including five passes for 99 yards to Green.