Kavin Gilder-Tilbury, who made 7 of 11 field-goal attempts, added a career-high 16 points for Texas State (10-5, 4-2 Sun Belt). Ethan Montalvo scored 14 and D.J. Brown 12.
Ken Williams hit a 3 with 18:10 left to pull South Alabama (4-12, 2-4) within three, but Montalvo hit a pair of 3-pointers during a 15-3 run which made it 55-41 about 5 minutes later.
The Jaguars trailed by double digits the rest of the way.
South Alabama shot 54 percent from the field and made nearly twice as many free throws (27) as Texas State attempted (15), but it wasn't enough.
Texas State converted 15 offensive rebounds into 17 second-chance points and scored 26 off of 19 South Alabama turnovers.
Williams led the Jaguars with 23 points.