Adjehi Baru grabbed nine rebounds for the Cougars (3-4), who were outrebounded 34-25.
Charleston led 8-3 on a jumper by Cameron Johnson, but The Citadel regained the lead 29-28 on a free throw by Moore and led 33-28 at halftime.
Evan Bailey made back-to-back buckets and Charleston took a 36-35 lead in the second half. Moore tied it a 50 with two free throws, then hit a 3 to put the Bulldogs up 55-54 with 48 seconds to play. Gilmore hit a layup, drawing a foul from Quinton Marshall, then completed the three-point play for a 57-55 lead. Barry sealed the game with a dunk.