ASU (40-15) rebounded after being held scoreless in Tuesday's initial title game, to win the tournament with a 4-1 mark including a 45-8 advantage in runs scored.
The Rams, who were the top seed as the LSC Champions by virtue of the best regular season record, scored five runs in the second inning to take control of the game.
Brett Parsons started the frame with a base hit, before scoring on Doug Snover's double to left field. Andrew LaCombe then singled through the right side to plate Lee Neumann, who reached on a fielder's choice, and Snover. Tate Allison delivered the final two runs with his fifth home run of the season.
ASU added one more run in the third, when Snover singled to bring Neumann, who had reached on an error, home.
Michael Lange (9-0) earned the victory for the Rams, allowing three hits in five innings with three strikeouts. Michael Weatherly and Craig Blair also saw action in the combined shutout effort.
Tarleton (30-21) managed eight hits but left seven on base. Matt Buckmaster (6-2) took the loss for the Texans.
The all-tournament team included seven players from ASU and four from Tarleton.