Knowshon Moreno rushed for a career-high 157 yards in his first start for Georgia (5-2, 3-2 Southeastern Conference), who danced on the Vanderbilt (3-3, 1-3) star at midfield after Coutu's kick sailed through the uprights.
Georgia coach Mark Richt pushed his players away from the midfield celebration after the game. Vanderbilt defeated the Bulldogs in Athens last year.
Vandy's Cassen Jackson-Garrison fumbled 7 yards short of the goal line, setting up the Bulldogs' winning drive.
Matthew Stafford had 201 yards passing for Georgia, including a 32-yard touchdown pass to Sean Bailey.
Former Jefferson County star Sean Walker caught a touchdown pass and ran for another for Vanderbilt, who didn't score a point in the second half.
Walker caught a 16-yard touchdown pass, originally ruled incomplete, to give the Commodores a 17-7 lead in the third quarter. Walker bobbled the ball twice, but appeared to control it before falling out-of-bounds in the back of the end zone.
Vanderbilt essentially found themselves playing a road game with Georgia fans painting Vanderbilt Stadium red in a rare sellout.
Stafford led the Bulldogs on a 10-play, 73-yard drive to set up the field goal by Coutu, his second of the game. Coutu also kicked a 31-yard field goal earlier in the fourth quarter.
Vanderbilt swapped quarterbacks early before sticking with backup Mackenzie Adams.
Adams had 125 yards passing and a touchdown, and he also ran for 76 yards on several option plays. Chris Nickson made his 18th consecutive start for Vanderbilt, but saw limited action after the first quarter. Nickson went just 2-for-5 for six yards.
The Commodores tricked the Bulldogs most of the night, pulling several reverses and deceiving plays.
D.J. Moore had 123 all-purpose yards.
Moreno had a 32-yard rush to setup a Georgia touchdown on the opening drive of the second half, narrowing Vanderbilt's lead to 17-14.
Georgia tailback Kregg Lumpkin left the game in the third quarter with an ankle injury, putting even more of a burden on Moreno - who was already replacing injured starter Thomas Brown.