Reed Trimmer scored a career-high 30 points for Drake (4-5).
Drake's Graham Woodward hit a 3-pointer and Trimmer made two free throws to cut the Bulldogs deficit to 71-68 with 19 seconds left in the game.
But Myke Henry hit three of his four free throws in the final 15 second for DePaul to push the lead back to 74-68 and effectively ice the game. Woodward hit a final 3-pointer as time expired.
The Blue Demons led 38-37 at the break and trailed for only 18 seconds in the second half, after a layup by Drake's Jacob Enevold Jensen briefly gave the Bulldogs a 41-40 lead.