Charles Sims had 207 yards and two scores 17 win over Tulane.
Case Keenum went 22-for-29 with 325 yards and all three of his touchdown passes went to Patrick Edwards, who finished the game with five catches for 129 yards for the Cougars (10-0, 6-0 C-USA), who have averaged 61.7 points in their six conference wins.
Edwards also had a punt return for a touchdown as did Damian Payne for Houston.
Orleans Darkwa had 21 carries for 123 yards and two touchdowns for the Green Wave (2-9, 1-6), who have lost their past eight games. Ryan Griffin went 19- for-43 with 137 yards and an interception in the loss.