The Chanticleers raced to a 44-23 lead by intermission, with Shaw knocking down three 3-pointers in the final 7:01 to cap the period.
Elijah Wilson hit a pair of 3-pointers in the opening minutes of the second half but Charleston Southern had a 10-0 run that cut the lead to 54-42 with 13:15 remaining in the game.
Wiggins was 6 of 9 from the field and 9 of 11 from the line to finish with 23 points for the Chanticleers (11-8, 5-4 Big South). Shaw with 8 of 16 from the field, including 3 of 7 from beyond the arc, for 22 points.
Javis Howard scored 15 points to lead the Buccaneers (8-12k, 4-5), and Armel Potter added 14.