Stauskas said his first thought was to go to the rim, but that defender Nigel Hayes was overplaying him.
"He kind of slid forward a little bit and I was open for 3 and I just tried to be aggressive and shoot it," Stauskas said.
Caris LeVert added 20 for the Wolverines (13-4, 5-0 Big Ten), who celebrated a victory in Madison for the first time since 1999.
But wins usually don't come easy at the Kohl Center for any team, and the Badgers (16-2, 3-2) made it difficult for Michigan in nearly overcoming a 15-point deficit.
Wisconsin went on a 14-2 run late, and Ben Brust's putback got them within 68-67 with about 2 minutes left.
But after whiffing on a 3 from the right wing, Stauskas hit his step-back 3 from the left side to give Michigan a 71-67 lead.
"That step back is so fast, and that release is so fast," coach Bo Ryan said. "He's quick, he's like a cat."
Josh Gasser had 16 points for the Badgers, who lost their second straight after a school-best 16-0 start.
No. 2 Syracuse 59, No. 22 Pitt 54 • In Syracuse, N.Y., Freshman point guard Tyler Ennis scored 16 points, including two driving layups and two free throws in the final 2 minutes, in a battle for first place in the ACC between the two former Big East rivals.
Syracuse (18-0, 5-0 Atlantic Coast Conference) entered the game 2-0 against former Big East rivals, with victories over St. John's and Villanova.
No. 15 Kansas 80, No. 9 Oklahoma State 78 • In Lawrence, Kan., Naadir Tharpe scored 21 points for Kansas, and Frank Mason stripped Oklahoma State's Le'Bryan Nash as the final buzzer sounded to preserve the win.
Joel Embiid added 13 points, and 11 rebounds for the Jayhawks (13-4, 4-0 Big 12).