The Dragons (9-14, 7-5 Colonial Athletic Association) pulled within a game of Northeastern (16-9, 8-4) for third place in the association.
Drexel led 27-18 at the break. Allen scored five straight points, and Rodney Williams had a dunk to stretch Drexel's lead to 49-31 with 6:19 remaining, and the Dragons cruised from there.
Anthony Stitt scored 15 points to lead Charleston (7-18, 2-10). The Cougars, who snapped a five-game losing streak Thursday night with a win over CAA leader William & Mary, was held under 49 points for the third time.