Hardaway hit a contested 3-pointer to put the Wolverines up 65-52 with less than 3 seconds left in regulation. Brust collected the inbounds pass near halfcourt, took one dribble and hit a runner that touched nothing but net to tie the game.
Wisconsin and Michigan traded baskets in overtime before Brust hit the 3-pointer over Caris LeVert to put Wisconsin up 65-62 with less than 40 seconds left.
Hardaway couldn't connect on his drive to the hoop on the next Michigan possession, and Glenn Robinson III fouled Berggren on the rebound.
The Wolverines went to a full-court press with two more fouls to give. But the Badgers broke the press, and Michigan had to commit two more fouls to finally put Ryan Evans on the free throw line.
Evans, who shoots less than 43 percent from the line, missed the front end of a 1-and-1, and Burke couldn't connect in a rushed final possession for the Wolverines.
It was another grinding win for the Badgers keyed by their defense. Michigan came in as one of the top scoring teams in the country at almost 78 points per game. But Wisconsin held Michigan to less than 40 percent shooting from the field, including 5 of 18 from beyond the 3-point line.
The win extended the Badgers' 11-game home winning streak against Michigan, the best in school history.
It was the second straight game for both teams to go past regulation. The Badgers beat Iowa 74-70 in double overtime on Wednesday, while Michigan beat Ohio State 76-74 in overtime on Tuesday.