The Buccaneers have won three straight in the Big South Conference, following a three-game losing streak.
Wheeler hit 1 of 2 free throws to give Charleston Southern (8-11, 4-4) a 71-69 lead with 51 seconds left.
Three possessions later, Presbyterian's Reggie Dillard hit a layup and was fouled by Charleston's Melvin Brooks and, after hitting the free throw, gave the Blue Hose a 72-71 lead with 15 seconds to go.
However Potter was fouled by Davon Bell on the Buccaneers' final possession, setting up his game-winning free throws.
Dillard had a final shot at the buzzer to win it, but missed.
Potter and Patrick Wallace scored 13 apiece for Charleston Southern.
DeSean Murray led Presbyterian (8-11, 3-5) with 17 points.