Cunningham's jumper with 3:39 to play in OT put SC-Upstate (8-16, 2-5 Atlantic Sun) on top for good at 80-78.
Hampton-who finished with 17 points- drove the lane but lost the ball out of bounds with three seconds remaining.
At the end of regulation, Nathan Moran made three free throws after getting fouled on a 3-point shot attempt with a second left to tie it at 76.
Six seconds prior, Moran made two of three free throws-again after getting fouled on a 3-attempt-to reduce Lipscomb's (7-17, 3-4) deficit to 74-73.
Cunningham made two free throws with four seconds left for a 76-73 lead.