Pat Swilling Jr. added 12 points and Kauri Black had 10 for the Golden Hurricane (10-7, 2-1 Conference USA), who shot 53 percent from the field and outrebounded the Owls 36-21.
Tamir Jackson led Rice (3-12, 0-2) with 14 points, and Seth Gearhart had 12.
The game was tied 51-51 after Rice’s Max Guercy hit a layup with 4:49 remaining. Tulsa scored on its next three possessions, getting two free throws from Scottie Haralson, a dunk by Harrison and a layup from Black to go ahead for good.
Rice committed four turnovers and missed all four of its shots after Guercy’s layup, while Tulsa closed it out by making 7 of 8 free throws in the final five minutes.