Purdue's struggles from the free throw line also continued, as it missed 7 of its 16 attempts.
Roberto Nelson added 10 points for the Beavers (3-1), who squandered a 15-point cushion in the second half before taking over again in the final two minutes.
Oregon State dominated the boards 47-36 and overcame an apparent knee injury to center Angus Brandt, who had nine points and nine rebounds.
The score was tied at 56 with 2 minutes to play when Collier put Oregon State ahead to stay by sinking a pair of free throws to start a decisive 8-0 run.
Boilermaker freshman post A.J. Hamons had a strong outing, as he scored a team-best 20 points and also led Purdue with eight rebounds.
Boilermaker guards D.J. Byrd and Anthony Johnson chipped in 11 and 10 points, respectively in the loss.