Robert Nyakundi added 13 points for the Mustangs (7-10, 1/3 Conference USA).
Two free throws by Kuipers pulled Rice to within 69-65 with 30 seconds remaining, but the Owls failed to score again, missing two 3-pointers. SMU then hit 4-of-6 free throws to secure the victory.
The game was tied 34-all after a first half which featured six lead changes and six ties. The Mustangs scored the first three points of the second half and never trailed again.
Neither team led by more than eight points.