Caracter's dunk coming out of a UTEP timeout after UAB's Aaron Johnson had tied it 50-50 with six seconds left proved to be the game-winner.
Caracter ended with 13 points and six rebounds while Myron Strong added 15 points as UTEP (24-5, 15-1 C-USA) closed its regular season on a 14-game winning streak and claimed the top seed in next week's Conference USA Championship tourney in Tulsa.
In the tourney, UTEP will play the winner of Wednesday's game between the eighth- and ninth-seeded teams.
Johnson led UAB (23-7, 11-5) with 16 points while Elijah Millsap chipped in with 12 points and hauled down 14 rebounds in the loss.
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