Both teams struggled offensively as UAB (18-10, 7-7 Conference USA) shot 36 percent from the field (21 of 58) and 13 percent from 3-point range (1 of 8) and Rice finished 24 of 61 from the floor (39 percent) and 6 of 27 from deep (22 percent). The Blazers, however, got the free throw line 23 times, converting 18 while Rice was 6 of 9 from the charity stripe - falling to 2-16 this season when attempting fewer free throws than its opponent.
Sean Obi's jumper with 34 seconds left gave Rice a 60-57 advantage before Fahro Alihodzic cut the Blazers' deficit to one with a layup 12 seconds later. C.J. Washington's block on the other end set up Frazier's game winner.
Obi led Rice (7-20, 2-13) with 12 points.