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).