Curtis Reed carried the Cougars to a third-place finish on Sunday at the Border Olympics in Laredo.
The sophomore finished eighth individually after shooting two-over at the par-72, 7,319-yard course at Laredo Country Club.
Reed shot par in the first and final rounds, and two-over in the second round.
The Cougars paced the 16-team field after the first round with a score of 290, but finished the tournament 18 strokes behind first-place Lamar and 13 strokes behind second-place Baylor.
Junior James Ross finished tied for 16th for UH.
Freshmen Roman Robledo and Kyle Pilgrim tied for 29th place.