Hollins drained a go-ahead 3-pointer with 3 1/2 minutes remaining in the extra frame and the Golden Gophers (18-7, 6-6 Big Ten) were never headed after that.
Austin Hollins added 11 points and four assists while Rodney Williams provided 10 and five rebounds in the victory.
Sam Dekker notched 14 points and four boards as the Badgers (17-8, 8-4) saw their three-game winning streak snapped.
Ben Brust also reached double figures with 10 points for Wisconsin, which went 7-of-28 from 3-point range.
Rosie O'Donnell unveils nearly 50-pound weight loss
Members of Congress to keep receiving porn magazine