Austin Poganski and Jordan Nolan scored 31 seconds apart for a 2-0 Rampage lead at 6:34 of the third period, and Dakota Joshua scored into an empty net at 18:22 for the 3-0 final.
Ville Husso made 19 saves for his fourth shutout of the season for San Antonio (24-21-7-5), which won its season-high fifth straight game and moved into sole possession of third place in the Central Division.
Matt Tomkins made 24 saves on 26 shots for the IceHogs (28-29-1-2), who went 2-3-0 during their five-game road trip. It was Tomkins’ first start since allowing six goals and getting into a fight Feb. 22 at Milwaukee.
Dylan Sikura, who hasn’t scored a point in six games since his career-high 11-game point streak ended, recorded a team-high four shots on goal.
The IceHogs, who were shutout for the sixth time this season, went 0-for-2 on the power play and are 0-for-25 in their past seven games.
The IceHogs have a three-in-three weekend, starting with a home-and-home against the Grand Rapids at 6 p.m. Friday.