Houston trailed by only four as the game reached the midway point of the first half, but Memphis pulled away to a 15-point advantage at intermission and was not threatened in the second period.
Goodwin hit 8-of-13 shots from the field and scored 20 points while Joe Jackson contributed 18. The Tigers made 61 percent of their field goal attempts and forced 17 turnovers.
Memphis improved to 14-4 for the season and to 4-2 in the American Athletic Conference.
TaShawn Thomas had 14 points for Houston (11-8, 3-3 AAC).