DeVince Boykins made a 3 to stretch the Eagles' lead to 61-55 with seven minutes remaining. Frederic Dure made a pair of free throws, Anthony Livingston scored seven straight points and Arkansas State led 64-63 with 2:25 left.
Hughes and Brown answered with consecutive 3s and the Eagles regained the lead, 69-66, with a minute to play. Sean Gardner missed a potential game-tying 3-pointer with 16 seconds left, and Hughes made two free throws to seal it.
Ike Smith added 11 points for Georgia Southern (8-12, 4-6 Sun Belt Conference).
Gardner hit three 3-pointers and finished with 20 points to lead Arkansas State (10-11, 6-4). Livingston added 16 points.