Cunningham had a double-double, 18 points and 10 rebounds, and Keith Hornsby added 17 points to help UNC Asheville (12-10, 6-2 Big South Conference) win its fourth-straight game.
Trailing 68-60 with 5:25 remaining, Presbyterian went on a 12-5 run to take a 72-71 lead on Khalid Mutakabbir's free throws with one minute left to play.
After Hornsby answered with a jumper to put UNC Asheville ahead 73-72, Joshua Clyburn's layup gave the Blue Hose a 74-73 lead with 30 seconds to go.
With 11 seconds left to play, Cunningham gave the Bulldogs the lead for good with a layup to make it 75-74. Hornsby added two free throws, and Mutakabbir missed a 3-pointer as time expired.
Mutakabbir scored 21 points for the Blue Hose (5-17, 2-6).
Officials: North Carolina must show proof of discrimination-free zone, or lose NCAA tournament games
North Carolina must prove to the NCAA that its host arenas will provide a discrimination-free zone or risk losing NCAA tournament games in 2017 and 2018, multiple officials told ESPN.
Jalen Rose and David Jacoby examine the new NCAA draft rule and consider how it would have affected "The Fab Five."
Florida and Duke will meet on Dec. 6 in the Jimmy V Classic at Madison Square Garden as one of two high-profile games to help raise funds for cancer research.