The Cougars (3-0) hit 10 of their first 15 shots after halftime to build a 64-49 lead with 10:43 remaining.
Arkansas (2-1) chipped away at the lead and pulled within 72-68 on a Julysses Nobles steal and slam dunk with 4:16 to play, but could get no closer.
The Razorbacks led by as many as eight points late in the first half, but the Cougars ended the period on a 10-2 run to tie the game 36-36 at halftime.
Houston hit 18 of 23 free throws and scored 19 second-chance points to stymie the Razorbacks’ comeback bid.
Arkansas was playing without leading scorer and rebounder Marshawn Powell, who suffered what Razorbacks coach Mike Anderson called a “severe knee injury” in practice Thursday.
Nobles led Arkansas with 16 points.