After Harris' 3 put the Blue Raiders (3-1) up 63-59, Dylan Smith answered with a jumper for Asheville (2-4) with 22 seconds left. But Middle Tennessee avoided a clock-stopping foul until the final second and escaped after squandering a 19-point, second-half lead.
Middle Tennessee led 51-32 on Perrin Buford's 3-pointer with 12:56 left. The Bulldogs then went on a 23-4 run to get even at 55 but never pulled in front.
Dylan Smith had 14 points to lead the Bulldogs, who face Loyola-Chicago for third place.