The Hilltoppers (3-2) led nearly the entire night, but needed to make several clutch plays late to hang on.
P.J. Thompson hit a corner 3-pointer with 5.8 seconds remaining to bring the Boilermakers (4-2) to 75-73, but Thompson answered with two free throws that made it a two-possession game and all but sealed the win.
Justin Johnson led the Hilltoppers with 17 points, including a tough driving score for a five-point lead with 21 seconds left.
Isaac Haas scored 22 points to lead Purdue, which shot just 32 percent in the first half. The Boilermakers trailed 42-31 at the break and never fully recovered.