The Miners (21-5, 12-1 Conference USA) led 58-53 after Caracter's jumper from the top of the key with 53 seconds left, but a 3-pointer by Gary Flowers, who led Southern Miss with 15 points, made it 58-56 six seconds later.
Angelo Johnson got a steal for the Golden Eagles (16-11, 6-7) on the ensuing possession, but a couple of missed jumpers gave the ball back to UTEP. Culpepper's free throw with 13 seconds left gave the Miners their final margin.
Southern Miss' Josimar Ayarza's 3-point attempt at the buzzer rimmed out.
UTEP opened the second half with a 15-6 run to lead 45-35 with 10:32 left. But Southern Miss wouldn't go away, putting together an 18-6 run in the final 7:36 to keep the game close.