The 20th-ranked Tigers, who improved to 3-0 overall, were led by sophomore guard Alli Smalley, who scored 18 points.
Senior DeWanna Bonner added 11 points for the Tigers and freshman Chantel Hilliard chipped in with 10 points and six rebounds.
The Tigers outshot the home team 47.5 percent to 28.1 percent.
The Tigers led by just two points late in the first half, but managed to stretch their margin to 36-27 by intermission. Auburn scored nine of the first 11 points of the second half and was never threatened after that by the Eagles, who fell to 2-1 with their first loss.
"That first half was not pretty," said Auburn coach Nell Fortner. "When we went into halftime we made some adjustments."
The coach noted the Tigers had success running their halfcourt in the final 20 minutes.
Auburn hit 2-6 threes and struggled at the foul line making just 11-25 free throws.
Georgia Southern hit 5-24 threes, 8-18 free throws and turned the ball over 20 times, one more than Auburn. The Tigers out-rebounded the Eagles 50-39.
The Tigers return to action with a 2 p.m. home game on Sunday vs. 17th-ranked Ohio State in a battle of nationally-ranked teams. The Tigers knocked off the Buckeyes last season in Ohio.