Soza had scoring throws of 29, 5 and 34 yards while completing 15 of 30 passes for 200 yards. He also rushed for 97 yards, including a 2-yard touchdown that put the Roadrunners (8-4, 3-3 Western Athletic) up 31-14 early in the second half.
Texas State (3-8, 1-4), which concludes its season Dec. 1 against New Mexico State, got three touchdowns from quarter Shaun Rutherford. He completed 31 of 42 passes for 324 yards and two touchdowns, but was also sacked five times by UTSA. Rutherford also ran for a 2-yard score.
Isaiah Battle had seven receptions for 119 yards for the Bobcats, including a 57-yard TD.
UTSA, which won its third straight, also scored on a 79-yard punt return by Kenny Harrison.