Devonta Pollard had 12 points and 10 rebounds, Danrad Knowles scored 11 and Damyean Dotson finished with nine points and nine rebounds for the Cougars.
Houston (14-6, 4-4 American Athletic Conference) opened the game on a 9-0 run and Gray's 3-pointer with 12:26 left in the first half sparked a 16-2 spurt that made it 31-14 about 5 1/2 minutes later.
The Cougars led by as many as 21 before taking a 40-27 lead into halftime.
Houston led by double figures throughout the second half.
Tulsa (13-7, 5-3) committed a season-low five turnovers, but couldn't overcome its poor shooting. The Golden Hurricane shot just 32.8 percent, including 3 of 26 (11.5 percent) from 3-point range.
Pat Birt scored 16 and Shaquille Harrison added 15 points for Tulsa.