Oveneke added 11 points for Drexel (12-8, 5-12 Colonial Athletic Association) and Scott Rodgers and Jamie Harris each chipped in 10 points.
Juwann James scored a game-high 22 points for James Madison (12-16, 4-13), which lost for the fifth time in six games. Jalloh and Kyle Swanston had 12 points each and Terrance Carter added 10 points for the Dukes.
Hawthorne's free throw with 2:04 left in the game put the Dragons ahead 65-58, but Abdulai Jalloh banked in a 3-pointer to cut the margin to 68-67 with 16.8 second left. Rob Hampton's layup put Drexel up 70-67 with 13.2 seconds left.
James Madison led 32-30 at the half, but the Dragons went on a 10-0 run early in the second period, capped by Hawthorne's 3-pointer with 18:39 remaining. Another Hawthorne trey capped a 15-4 run that gave the Dragons an 11-point lead with 4:28 to go.
