Potter was 6 of 13 from the floor and added four rebounds and four assists. Patrick Wallace scored 14 points and Raemond Robinson added 12.
Charleston Southern (3-5, 1-1 Big South) was up by one at intermission, but a 10-1 run at the start of the second half, punctuated by Robinson's 3-pointer, gave the Buccaneers a 41-31 lead at the first TV timeout after the break.
Liberty (3-6, 0-2) cut its deficit to five on an Ezra Talbert layup with 8:54 left, but the Bucs scored the next five points and held off Liberty down the stretch.
A.C. Reid led Liberty with 20 points and was 5 of 11 from beyond the arc. Evan Maxwell had 14 points with eight boards and Anthony Fields scored 10.