The score was tied at 30 early with 15:23 left when Peterson scored all eight of his points in a 12-2 burst.
Michigan State (26-4, 15-1) won for the 22nd time in 23 games heading into the conference tournament at Chicago this week. The Spartans are hoping to lock up a No. 1 when NCAA bids are awarded next Sunday.
Purdue (19-11, 7-9) saw its hopes for a seventh consecutive NCAA appearance diminish. The Boilermakers would need four victories in the Big Ten tournament to get the conference's automatic bid.
Antonio Smith scored all 12 of his points in the second half for Michigan State. He also had eight rebounds as the Spartans dominated the boards 39-20.
After Purdue tied it for the last time at 30 on a fastbreak layup by Maynard Lewis, Peterson hit a jumper to put the Spartans ahead to stay.
Peterson made two more jumpers and two free throws as Michigan State built a 42-32 lead. He leads the Spartans in scoring, though he has started only three times this season.
Greg McQuay, who led Purdue with 12 points, pulled the Boilermakers to within 42-34 with 10:09 remaining. Purdue was unable to draw any closer.
Purdue scored the game's first seven points, delighting most of the partisan sellout crowd of 14,123. Mateen Cleaves quickly got the Spartans back into the game with a 3-pointer and a jumper and Michigan State tied the game for the first time t 13.
Michigan State held a 24-21 edge at halftime.
Cleaves finished with eight points, failing to reach double figures for the second consecutive game. He did all his scoring in the first half and acted as a decoy for most of the second half, taking just one shot.
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