Aldridge nailed a 3-point jumper and Oskar Michelsen followed with two free throws for a 78-76 lead with 5:17 left. Cameron Johnson, who scored 13 points, answered with a trey and Jarrell Brantley followed with a layup to give Charleston an 81-78 lead.
Andrew McAuliffe drove for a layup to trail 81-80 with 2:12 left. Brantley fouled Aldridge and he made both free throws for the win.
Davidson was up 52-45 at the break but the Cougars charged back to lead 56-54 following a Canyon Barry 3-pointer with 16:39 left. Barry finished with 31 points on 12-of-24 shooting from the floor for Charleston (2-1).