Tarik Black came off the bench to score nine points for Memphis (26-4, 14-0 C-USA), including the decisive dunk with 2:21 to play and a big rebound in the closing seconds.
The Miners (16-13, 9-6) missed four free throws and a 3-point shot in the final minute. Julian Washburn led UTEP with 19 points and Cedrick Lang scored 10 points and collected seven rebounds.
Memphis shot 42.3 percent from the field to 42.2 percent for UTEP. The score was tied 22-22 at halftime.