Damian hit her solo shot over the right field fence in the sixth inning while Tucker's home run went to center field.
Sam Houston (1-12) totaled three hits with designated hitter Cecilla Castillo hit a double in the fourth inning.
Longhorn designated hitter Courtney Craig led Texas at the plate going 2-for-4 with three RBIs.
Rachel Fox (5-0) was the winning pitcher for Texas. Shelby Lancaster (0-4) started for Sam Houston, facing 26 batters in four innings. Haley Boros threw the final two innings.