Channing Toney added 12 points and Lawrence Kinnard had 11 for UAB (17-7, 7-2 Conferece USA).
Patrick Britton led Rice (3-20, 0-10) with 18 points and 10 rebounds. The Owls played their fifth consecutive game without leading scorer and rebounder Paulius Packevicius, who is out with a knee injury.
Rodney Foster scored 12 points and Lawrence Graham added 10 for the Owls.
UAB shot worse than Rice from the field but made up for it at the foul line and from behind the 3-point arc. The Blazers made 21 free throws and hit eight 3-pointers, which both at least doubled those made by the Owls.
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