The Cougars led the Green Wave by one, 29-28, at the half. But Houston (18-4, 7-1 C-USA) forced 12 turnovers and hit eight 3-pointers as it outscored Tulane 37-28 in the second half.
Tulane (15-8, 5-4 C-USA) shot 52.4 percent from the field, to Houston's 32.4 percent, and grabbed more rebounds. But 12 of the Cougars' 22 total field goals were 3-pointers, and Tulane hit a season-low 45.8 percent from the free-throw line.
David Gomez led Tulane with 17 points.