Stauskus added four foul shots in the final 24.7 seconds to seal Michigan's seventh straight win. He had 16 in the second half.
The Wolverines benefited from the cushion built from a first half in which they shot 60 percent. That's especially impressive given it was against Wisconsin, perennially one of the league's best defensive teams under coach Bo Ryan.
But defense was a problem again for the Badgers in their second straight loss after allowing Indiana to shoot 51 percent earlier in the week.
Still, the Badgers came back, bolstered by boisterous students back in town for the spring semester. The Kohl Center was rocking after the Badgers' late run, during which Michigan at one point missed four shots and committed two turnovers.
Nigel Hayes' short jumper got Wisconsin within six with 4:45 to go before Brust put back his own rebound to get Wisconsin within a point.
That's when Michigan turned to Stauskus. His first 3-point attempt glanced off the rim but Michigan retained possession after a foul was called on Gasser.
The ball went back to Stauskus, who shook off Hayes on the perimeter and coolly hit his 3 for a late four-point lead.
Glenn Robinson III added 14 points on 6 of 8 shooting for Michigan, while Brust finished with 14 points and eight rebounds.
Michigan also took advantage of uncharacteristically sloppy play by the usually savvy Badgers, stretching a five-point halftime lead to as much as 15 midway through the second half.
Brust shot an airball coming out of a timeout, and Jon Horford hit a short hesitation jumper to make it 51-40 with about 14:40 left.
Stauskus later pumped his arms after hitting a 3 from the wing for Michigan to get the lead to 13.
The Wolverines are off to their best start in conference since opening the 2002-3 season 4-0 in the Big Ten. They got a huge boost at the start of a tough three-game stretch against ranked opponents, with games against Iowa and Michigan State coming up next week.