The Tigers won their 17th straight game, opening a 14-point lead with 3 minutes remaining and easily holding off a late Houston charge.
Memphis is 23-3 for the season and advanced to 12-0 in Conference USA. The Tigers hold a two-game lead over Southern Mississippi, a team it will host on Saturday.
Tank Black added 15 points off the bench for the Tigers and D.J. Stephens had 14 points to go with 10 rebounds.
Memphis went on a 26-11 run during the middle stages of the second half to break open the contest. It was the Tigers' 19th straight league victory.
Houston (15-10, 4-8) was led by Joseph Young with 22 points.