The Cougars (12-11, 4-6 Conference USA) led most of the way and by as many as 17 points late in the second half. Houston shot 51.9 percent from the field and took a 40-30 advantage on rebounds.
Zamal Nixon led the Cougars in scoring with 17 points, including making all of his 11 tries from the free-throw line. Alandise Harris added 11 points for Houston while Adam Brown and Kendrick Washington each scored 10.
The Green Wave (12-12, 2-9) scored the first eight points of the game, but the Cougars answered with an 15-3 run and never trailed again.
Jordan Callahan led Tulane with 18 points while Kendall Timmons and Johnny Mayhane scored 15 each and David Booker scored 10.