Marcus Malone added 17 points and Kelvin Lewis had 11 for the Cougars (21-6, 10-3 Conference USA). Tafari Toney had 12 rebounds for Houston.
Craig Craft came off the bench to lead Southern Miss (15-12, 7-6) with 16 points. Courtney Beasley and Andre Stephens each had 14 points.
The Cougars used a 17-6 run, including 16 straight points by McKiver, to take a 26-13 lead midway through the first half.
McKiver's 52 points is the most for the Cougars since Elvin Hayes scored 55 against Southwestern on Feb. 12, 1966.