Chelf went 17-of-22 through the air, hooking up with Charlie Moore, Blake Jackson and Blake Webb on scoring strikes for the Cowboys (8-5).
Fellow quarterback J.W. Walsh also found the end zone twice, completing TD tosses to Isaiah Anderson and Jeremy Seaton as Oklahoma State won a bowl game for the third straight season.
The Boilermakers (6-7), meanwhile, were led by Robert Marve, who was intercepted twice while tossing for 212 yards and a pair of scores in the loss.
Purdue saw its two-game bowl-winning streak ended with the defeat.