In the first half, Houston guard Jamal Shead earned a career milestone by becoming the fourth Cougar to reach a total of 600 assists in program history.
At halftime, Houston led the way over Texas, 40-27.
Cougar guard L.J. Cryer led the team in scoring, finishing the game with 26 points, including six treys. Shead finished with an incredible 16 points, 11 rebounds, six assists, and six steals for the game.
On the other hand, Longhorns forward Dylan Disu recorded 16 points and seven rebounds. UT guard Chendall Weaver added 11 points and four rebounds.
Overall, UH outscored Texas at home and capitalized on the defensive end with seven blocks and 13 steals for the game.
The game also had an official attendance of 7,904, which is a record at the Fertitta Center.
After Saturday's win over UT, Houston improves to an overall record of 22-3 in the season and 9-3 in the Big 12 conference.
The Coogs look to maintain their perfect record at home against Iowa State on Monday at 8 p.m., which airs on ESPNU.