Wiedeman had 11 points and 11 rebounds as the Cougars (7-3) outrebounded the Buccaneers 46-36 and scored 21 second-chance points.
Charleston made four of its five first-half 3-pointers in the first 10 minutes, and led by as many as 13 three times in the first half.
In the second half the Cougars grabbed 13 offensive rebounds for 11 second-chance points. Charleston used an 11-2 run to take a 21-point lead, 47-26, with 17:02 to play.
Donovan Monroe added 16 points and Jeremy Simmons had 12 for the Cougars, who won their third straight.