Trent Richardson rushed for 175 yards and scored three touchdowns to power Alabama.
The Crimson Tide (10-1) didn't win many style points in giving up a season-high 21 points, but the team's biggest national title boost came the previous night when No. 2 Oklahoma State fell 37-31 at Iowa State in two overtimes.
Alabama needed Richardson more than expected against the FCS Eagles (9-2). The Heisman Trophy candidate ran 32 times, caught a 4-yard touchdown pass and broke Shaun Alexander's school single-season mark of 19 rushing touchdowns.
He was still running well into the fourth quarter in a game that was expected to be a low-stress tuneup for the Iron Bowl at Auburn.
Georgia Southern's triple option attack burned the nation's top defense for 302 yards rushing.
No. 6 ARKANSAS 44, MISSISSIPPI STATE 17