Gant and Kavin Gilder-Tilbury scored five points each as Texas State (8-5, 2-2 Sun Belt) opened the game on a 14-1 clip.
South Alabama (6-10, 1-4) closed the gap to 35-32 at halftime and came as close as three points twice in the second half.
Texas State put the game away with a 16-4 run midway through the second half as Gilder-Tilbury, K.J. Malveau and Ethan Montalvo dropped consecutive 3-pointers. Montalvo, who had a second trey in the run, finished with 18 points and four 3-pointers.
The Bobcats outrebounded South Alabama 37-28 and had 15 assists on 28 field goals.