Barry made 8 of 13 field goals while Chealey was 6-of-8 shooting for College of Charleston (6-12, 1-4 Colonial Athletic Association), which shot a season-high 53.7 percent from the field. The Cougars came into the game shooting 40.7 percent.
Elijah Bryant made a layup and a pair of free throws to cap a 7-0 run and pull Elon (10-8, 2-3) within four with 13:12 left.
Barry responded with back-to-back 3's and layup to push College of Charleston's lead to 48-36.
After Bryant made two more free throws, Chealey scored five straight to ignite a 12-4 spurt to put the game out of reach.
Bryant led the Phoenix, who shot 39.5 percent from the field, with 19 points.