Houston 80, Prairie View 75
Houston (10-2) led by as many as 17 in the second half, but watched the Panthers claw their way back, cutting its lead to four after a Rasi Jenkins' lay-up made it 76-72 with 1:29 remaining in the game.
Daniel House, who scored 22 points while going a perfect 7 for 7 from the free-throw line, hit four free throws in the final 21 seconds to seal the deal for the Cougars. Houston was 21 of 26 from the line overall.
Joseph Young scored 17 points for the Cougars and Leon Gibson had 12 points and seven rebounds.
Jourdan DeMuynck led Prairie View (5-8) with 27 points on 10-of-21 shooting and Carl Blair scored 19 points, pulled five rebounds and had five assists.