Danuel House and Joseph Young added 23 points apiece for the Cougars (16-11, 5-9 Conference USA), who scored 106 points earlier this season in a victory over Louisiana College.
Houston shot 60 percent from the field and hit 8 of 15 3-point attempts while snapping a three-game losing streak.
DeAndre Kane scored 27 points and Elijah Pittman had 22 for Marshall (12-17, 5-9), which has given up 100-plus points three times this season. Dennis Tinnon added 13 points and 12 rebounds.
Houston scored the final nine points of the first half to take a 44-28 lead and increased that margin to as many as 32 points in the second half.