Chealey and Barry each scored six during a 17-5 run that extended the Cougars (5-4) from a one-point lead to 55-42 on Chealey's free throws with 54 seconds left in the game.
Barry also had eight rebounds and Anthony Stitt chipped in with 12 points for Charleston.
Campbell (3-6) used a 6-0 run to pull within 38-37 on D.J. Mason's free throws with 5:55 left in the game. Mason converted a three-point play with 4:01 left, but the Camels went scoreless until Mason's dunk in the final minute.
Mason had 13 of his 18 points in the second half and finished with six rebounds while Kyre' Hamer added 16 points.