HOUSTON (AP) Darian Thibodeaux scored 21 points, including a pair of free throws with 2 seconds remaining that gave Houston 76-75 victory over Rice on Saturday night.
Thibodeaux went to the free-throw line after Rice was issued a technical for calling a timeout it did not have with 2.7 seconds left.
Houston (15-14, 7-9 Conference USA) enters the conference tournament as the ninth seed and will face eighth-seeded UTEP on Wednesday. Rice (17-14, 8-8), seeded seventh, will face 10th-seeded East Carolina.
Houston surrendered a 13-point second-half lead to trail 74-73 with 16 seconds remaining on a layup by Arsalan Kazemi. Both teams traded a free throw before Thibodeaux's heroics.
Alandise Harris added 16 points for Houston and Jonathon Simmons had 12.
Kazemi led Rice with 19 points. Lucas Kuipers added 12 and Omar Oraby had 11.