ANN ARBOR, Mich. -- Michigan bolstered its chances of making the NCAA tournament for the first time in more than a decade.
"We hope this puts us in the tournament," Sims said. "But regardless, it was a big win for our program."
After losing a school-record 22 games last season, Michigan (18-11, 8-8 Big Ten) has given itself a chance to earn a spot in the NCAA tournament for the first time since 1998.
The Wolverines improved to 3-4 against ranked opponents and added an important victory to the ones it had over Duke and UCLA, when both teams were ranked fourth in the nation.
"We have to keep pressing on," coach John Beilein said. "But beating a Purdue team like this is great for us."
Michigan closes the regular season on the road against Wisconsin and Minnesota before playing in the Big Ten tournament.
Purdue, which had won four straight, fell two games behind Big Ten-leading Michigan State and a half-game behind Illinois.
"We pretty much eliminated ourselves from the race," Boilermakers coach Matt Painter said. "We're not mathematically out of it, but we'll need some help from Michigan State to make that last game in East Lansing matter."
The Boilermakers (21-7, 10-5) end the regular season at Michigan State after hosting Ohio State and Northwestern.
The Boilermakers trailed by three midway through the second half, but couldn't stop Sims or Harris during a 19-6 run that decided the game.
Michigan was 17-of-21 from the field in the second half (81 percent) and Beilein said he doesn't recall any team shooting that well in his three-plus decades as a coach.
After taking a 16-point lead with 4 1/2 minutes left, though, Michigan added some drama because it missed the front end of some 1-and-1 opportunities and missed a slew of other free throws in the closing minutes.
The Wolverines held on and their fans responded with a standing ovation for a program that is relevant again after being rocked by scandal and neglect.
Michigan surprisingly has a shot to end its NCAA tournament drought because of two talented standouts -- Sims and Harris -- recruited by former coach Tommy Amaker, gutsy freshmen and savvy coaching by Beilein, who is in his second season with them.
The Wolverines responded with a victory after a deflating loss to Iowa, the 10th-place team in the Big Ten, in which Harris was benched during the overtime.
"I don't want to worry about that," Harris said. "The only important thing is that we got this win."
Harris and the Wolverines bounced back with an inspired effort in their regular-season home finale.
Harris became the sixth player in Michigan history to reach the 1,000-point mark as a sophomore, joining Chris Webber, Jalen Rose, Phil Hubbard, Mike McGee and Louis Bullock.
The shooting guard forced Purdue to extend its defense with his outside shooting.
"He showed his full arsenal," Painter said. "He shot 3s, attacked the basket and made free throws."
Purdue struggled to defend Sims inside because 6-foot-10 forward JaJuan Johnson had three fouls midway through the first half and was called for a fourth early in the second.
"That was the difference in the game," Painter said. "JaJuan is the best shot-blocker in the Big Ten and when he's not in there, we don't have anybody to block or alter shots like he does."
Purdue's depth inside was impacted by the loss of 6-9 reserve Nemanja Calasan, who missed the game with a sinus infection.
Even though the loss seemed to dash the Boilermakers' hopes of winning the Big Ten title, they were encouraged by the play of their star player.
Hummel fell one point shy of his career high, showing he has regained form after missing three games earlier this month with a fracture in his lower back.
"The way he looked and played was the one positive we can take out of this game," Painter said. "He had spring in his legs and he was able to play a lot."
Hummel was healthy enough to play all but a minute of the intense game.
"This was a test for me, going 39," he said. "I felt as good as I have since I got hurt."