Jonathon Simmons scored 22 points and Alandise Harris added 18 points and eight rebounds as Houston defeated UTSA 77-75 on Tuesday night.
Darian Thibodeaux had 14 points for the Cougars (5-5), who scored eight straight points to take a 69-60 lead with 3:19 remaining and withstood UTSA's late surge.
Melvin Johnson III scored 24 points to lead the Roadrunners (5-5) and hoisted a potential game-winning shot with a second remaining. But his 3-point attempt missed.
Kannon Burrage scored 18 points and Jeromie Hill 15 for UTSA.
The Roadrunners scored eight points - on two 3-pointers by Hill and a Johnson jumper - to get within 76-75 with nine seconds to play. After Simmons made 1 of 2 from the free-throw line, UTSA got the ball to Johnson for the last shot.