In their first round match-up, 11-seed Houston took a 36-33 lead into halftime.
Although Marshall has a size advantage over Houston, Cougar forwards Alandise Harris (12 points) and Maurice McNeil (11 points) had big first halves. Marshall center Nigel Spikes took three fouls into the half.
While the Cougars outshot Marshall 56% to 38% in the half, they committed more turnovers (7 to 4) and were outrebounded (14 to 12).
The winner of this contest gets a second-round date with three-seed and tournament host UTEP on Thursday.