"We're getting better," he said. "I wish we were doing this six weeks ago."
Glenn Robinson III scored right out of the break, and Hardaway followed with a bucket to tie the score at 34 in the opening minute of the second half.
In a significant change of momentum, Burke stole the ball from Dru Anthrop, but Davis stole it right back, scored and was fouled to give Purdue a 41-34 lead.
Matt Vogrich hit a 3-pointer to cut Purdue's lead to 45-39, but the Boilermakers responded with a 3-point play and a layup by Terone Johnson to bump the lead to 11. Purdue's largest lead was 52-40.
Burke made a 3-pointer, then another bucket, to cut Purdue's lead to 52-45. Stauskas' 3-pointer with just over nine minutes left trimmed the Boilermakers' advantage to 54-48.
Michigan kept surging. A pair of free throws by Robinson made it a three-point game, and a free throw by Burke trimmed Purdue's edge to two.
Burke scored again on a floater that made it a one-point game.
A 3-pointer by Hardaway gave the Wolverines a 64-62 lead, and a 3 by Stauskas pushed Michigan's lead to five with 2:27 to play. The game tightened, but Purdue never led the rest of the way.
Beilein said overcoming Purdue's early surge was a challenge.
"I really applaud my coaching staff and my team for really staying united, for really helping everybody get through that," he said.