Ron Trapps scored 14 points, Shivaughn Wiggins added 11 and Badou Diagne grabbed 10 rebounds for the Chanticleers (12-8, 6-4), who entered fourth in the conference standings.
Wilson scored five straight points and the Chanticleers led 68-64 in overtime.
Ahmad Thomas hit a jumper with 1:28 remaining to pull the Bulldogs within 68-66, but Dylan Smith missed a potential winning 3-pointer with two seconds left.
Trailing by eight at halftime, the Bulldogs rallied to a 49-all tie on Will Weeks' layup with one second left in regulation.
Smith scored 14 with 10 rebounds, Weeks added 12 points while Sam Hughes had 10 and 11 rebounds for UNC Asheville (14-8, 7-3).