It was one point shy of Barry's career best and his third game with at least 30 points this season.
Marquise Pointer tied a career-high with 16 points, Cameron Johnson scored 15 and Payton Hulsey had nine points and a career-high 12 rebounds for Charleston (8-3), which has won six of its last seven.
D.J. Mason's layup with 7:50 left in the first half pulled Campbell (7-4) within two before Barry scored 10 during a 16-3 run that put the Cougars up 40-25 about six minutes later.
Charleston took a 45-27 lead into halftime and led by double figures throughout the second half. A 3-point play by Barry gave the Cougars their biggest lead, 63-36, with 10:59 to play.
Troy Harper scored a career-high 25 points for Campbell.