Marcus Sasser and Tramon Mark each had 12 points, and DeJon Jarreau had nine points for Houston (19-3). The Cougars shot 46%, including 13 of 31 on 3-pointers.
Houston forced the Hilltoppers (15-5) into 20 turnovers, which they turned into 27 points.
Taveion Hollingsworth had 17 points, and Charles Bassey added nine points and seven rebounds for Western Kentucky, which saw its six-game winning streak snapped. The Hilltoppers shot 42%.
Bassey, the Hilltoppers’ leading scorer with 18 points a game, was double-teamed throughout. He finished 3 of 7 from the field.
Trailing 40-39 early in the second half, Houston used an 18-2 run to take a 15-point lead on a 3-pointer by Jarreau with 13 ½ minutes remaining.