The Tigers (10-1, 6-1 Southeastern Conference) had blown a 27-7 lead but pulled out one more huge play to continue the biggest turnaround in major college football. From 3-9 last year, they can win the SEC West with a victory in two weeks against No. 1 Alabama.
Auburn's Nick Marshall heaved the ball downfield with two defenders around Louis. It bounced off safety Tray Matthews and Louis reached out his left hand to corral it.
Aaron Murray, who had engineered the comeback with three fourth-quarter touchdowns, could only stare helplessly from the bench. A win could have kept the Bulldogs alive in the SEC East.
Murray led Georgia (6-4, 4-3) all the way to Auburn's 20 but his final two passes fell incomplete as time ran out. Dee Ford hit him on the last pass as Murray ran toward the line before trying to throw.
Some Auburn players climbed into the stands to celebrate with students, and most fans stayed put to celebrate the victory.
It only came after Murray gave the Tigers a big scare. He had plowed into Ryan Smith at the goal line for a 5-yard touchdown with 1:49 left.
Auburn challenged the final TD, but replay officials upheld the call on the field.
That left the Tigers starting at their own 22 with 1:45 left. They managed one first down but Jordan Jenkins sacked Marshall to set up fourth and 18.
Marshall then produced the biggest play of his career against the Bulldogs, where he played as a freshman defensive back. He was dismissed from the team in February 2012 for violating team rules and returned to the SEC after a season in junior college.
He finished 15-of-26 passing for 229 yards after attempting only 15 passes combined in the past two games thanks to a steamrolling running game. Marshall also ran 19 times for 89 yards.
He also threw a game-winning TD pass with 10 seconds left against Mississippi State, but there was much more on the line this time. The 2010 national champions are potential contenders again.
Tre Mason ran 27 times for 115 yards, and Louis had his career game.
He caught four passes for 131 yards — nearly doubling the 160 yards he had entering the game — and gained 66 yards on five rushes.
It was just enough to survive Murray's furious onslaught.
The prolific Georgia passer completed 33 of 49 passes for 415 yards and two touchdowns in the final 9:35, with an earlier interception.
Murray also ran for two scores and had 160 passing yards in the fourth quarter.
Todd Gurley ran 15 times for 79 yards and a touchdown and caught 10 passes for 77 yards. Auburn gained 566 yards, Georgia 532.
The Tigers ran for 323 yards against a defense that came in giving up 126 yards a game on the ground, 20th nationally.
They had lost the last two meetings in the Deep South's oldest rivalry by 38 points apiece. Now, the Tigers hold a razor-thin 55-54-8 edge.
Auburn rode that punishing running game and Georgia mistakes to a 27-10 halftime lead, at one point outgaining the Bulldogs 170-4.
Cody Parkey hit three field goals and had a fourth blocked for the Tigers.