Reggie Upshaw had 12 points and grabbed 12 rebounds for Middle Tennessee (9-5, 1-1).
Middle Tennessee led most of the game until Dominic Artis nailed a trey with 15:02 left to give UTEP a 47-45 advantage. Harris answered with a jump shot and Upshaw hit another to give the Blue Raiders a 49-47 lead and they never trailed again.
UTEP closed to 74-72 with 26 seconds left following two Lee Moore free throws. Upshaw answered with a layup and Perrin Buford, who finished with 15 points, made two free throws in the final seconds to seal the win.
Moore, who scored UTEP's last nine points, finished with 20 and Terry Winn added 16 for the Miners (10-6, 2-1).