Barry was 6-for-14 from the field, but hit 13 of 14 at the foul line as the Cougars (6-2) made 22 of 29 free throws. Jarrell Brantley added 14 points on 7-for-12 shooting, and Cameron Johnson chipped in 12.
Charleston led all the way, going up by as many as 18 points just after halftime.
East Carolina (5-4) had a three-game winning streak end in its first visit to Charleston.
Kentrell Barkley hit 9 of 12 field goals to lead the Pirates with 22 points, 10 rebounds and five assists. It was the freshman's first double-double and first 20-point game. B.J. Tyson scored 17 points and Caleb White had 12 points.
Charleston will take a weeklong break for final exams.