Dylan Ennis had 10 points for the Owls (14-11, 5-5 Conference USA), who outscored Houston 16-7 over the final 5:23.
Omar Oraby scored seven points during a 9-0 Rice run that gave it a 72-64 lead with 2:35 remaining. Houston got no closer.
The Owls started the game in a hole, as the Cougars scored the first 13 points. Rice fought back to take a 26-25 lead on Reischel's 3-pointer with 3:07 left in the first half, and the teams stayed close until the final minutes.
Arsalan Kazemi, Rice's leading scorer and one of the top rebounders (11.0 a game) in the country, was limited to seven points and six boards.