Tim Hardaway Jr. added 13 points for Michigan, which has a chance to move to No. 1 in the next AP poll if it can win at Illinois on Sunday. Duke, the current top-ranked team, lost Wednesday.
The Wolverines (18-1, 5-1 Big Ten) trailed by seven in the first half, but Purdue (10-9, 3-3) couldn’t keep up its torrid outside shooting. Terone Johnson scored 14 points for the Boilermakers.
Michigan took control with a 14-2 run in the second half. The Wolverines have won 28 of their last 29 home games — the only loss was to Purdue last February.
Michigan trailed 33-32 at halftime after the Boilermakers shot 7 of 13 from 3-point range. Purdue then missed all nine of its attempts from long distance in the second half.
Glenn Robinson III — the son of the former Purdue star with the same name — made a 3-pointer to put the Wolverines ahead 42-40 and start Michigan’s decisive run. Burke gave Michigan some extra energy during one defensive sequence in which he nearly stole the ball at midcourt and then went diving on the floor to try to knock it free.
Mitch McGary eventually stepped in front of a pass for Michigan, bringing the crowd to life.
Another 3-pointer by Robinson made it 49-40, and it was 51-42 after a steal and layup by Burke.
Purdue trailed by as many as 11 before going on a brief run to make it 53-48. Michigan freshman Nik Stauskas answered with a 3-pointer from the left wing.
The Wolverines led 60-48 after McGary dunked on a fast break.