Sophomores Curtis Reed and Bryn Flanagan led the way for UH in the final round of play at the Royal Oaks Intercollegiate in Dallas.
The pair each shot 71s in the final round to help UH jump up a spot to tie for seventh in the 14-school field.
Junior James Ross, who was tied for second heading into the final round, shot a 74 to finish tied for ninth.
After a slow start, Ross finished the final nine holes with six pars, a birdie and two bogeys.