Michigan climbed within a game of Indiana for the top spot in the Big Ten Conference, overcoming a 12-point deficit with 12 minutes to play.
The Wolverines went in front for good on two free throws by Nik Stauskas with 3:04 to play and Burke went 7-of-8 from the foul line over the final 56 seconds to protect the lead.
Burke scored 26 points and Stauskas had 16. The Wolverines shot just 42 percent from the floor but turned the ball over a mere five times.
Michigan moved to 25-5 for the season and is 12-5 in conference play.
Terone Johnson led Purdue (15-15, 7-10) with 32 points. He went 12-of-17 from the field and made all five of his free-throw attempts.