Justin Gorham had nine points and 17 rebounds for Houston (15-1, 10-1 American), which won its 20th consecutive home game. Reggie Chaney added 10 points.
The Cougars won despite shooting only 34%.
Kendric Davis led SMU (9-4, 5-4) with 11 points. Feron Hunt and Yor Anei each scored 10 points for the Mustangs, who made 32% percent of their shots.
Houston led 28-24 at halftime, then went on a 14-3 run, capped by Gorham's three-point play with 16 minutes left.
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SMU: Coach Tim Jankovich missed his fourth straight game due to COVID-19 after first feeling symptoms on Jan.