Robert McKiver had 29 for Houston (22-8, 11-5), which had already secured the third seed in the tourney. Lanny Smith hit four 3-pointers and finished with 16 points for the Cougars.
UTEP (17-12, 8-8) had four players in double figures. Randy Culpepper had 16 points and Marvin Kilgore had 11.
The Miners, who shot a season-high 58 percent from the field, outscored Houston 11-1 in the final 2:15 after trailing by four with just under three minutes left to play.