The Tigers racked up 351 yards on the ground and limited Georgia Southern's option attack to 70 yards rushing.
Auburn quarterback Jarrett Stidham, a transfer from Baylor who was his making his first start for the Tigers, completed 14 of 24 passes for 185 yards with two touchdowns and an interception. He also rushed for a touchdown.
Auburn running back Kerryon Johnson finished with 136 yards, highlighted by a 60-yard touchdown burst in the first half, but suffered a leg injury on a long run in the second quarter and did not return.
Kam Martin stepped in and also rushed for 136 yards and a touchdown for the Tigers.
Georgia Southern freshman quarterback Shai Werts, making his first collegiate start, went 4 of 8 for 8 yards passing.
The Tigers started slow and committed three turnovers in the first half. Auburn led only 10-7 after Georgia Southern linebacker Tomarcio Reese scooped up a fumble and returned it 22 yards for a touchdown to put the Eagles on the board late in the first quarter.
Stidham completed only three of his first seven passes with an early interception, but the Tigers' running game and defense had his back.
Johnson, who started in place of the suspended Kamryn Pettway, gave the Tigers an early 10-0 lead on his 60-yard touchdown run, the longest of junior's career.
He broke free on another long run and seemed to be headed for the end zone but pulled up lame, went down and limped off the field with nine minutes left in the second quarter.
With Johnson on the sideline, Martin came in and quickly broke off a 36-yard touchdown run that put Auburn in front 24-7 late in the second quarter.
Georgia Southern managed only 37 yards of offense in the first half.
With the addition of Stidham and return of Pettway and Johnson, the Tigers are expected to contend with Alabama in the SEC West.
Auburn will find out more about how good it is next week when it travels to Death Valley to take on defending national champion Clemson. The teams met last year at Jordan-Hare Stadium, with Clemson winning 19-13.