The Roadrunners are 0-3-1 in their last four games and have scored only one goal in that stretch.
Eileen Albers, Sloane Popov and Lauren Pickup scored for Rice and Owls goalkeeper Kirsten Ruf recorded the shutout.
UTSA is now 0-2-1 in conference and 4-3-4 on the season.
The Roadrunners continue conference play on Thursday in Tampa against South Florida (2-5-3, 0-1-2), which lost to Florida Atlantic 3-0 on Thursday.
Rice is 4-5-3 on the season and 2-2-0 in conference.
