Burke stripped the ball from Keith Appling with 26 seconds left, leading to a go-ahead slam-dunk, then sealed the win with another theft with 2 seconds left as the Spartans sought a final shot.
Burke also dished off eight assists while Mitch McGary added 11 points for the Wolverines (24-5, 11-5 Big Ten), who bounced back from a shocking Wednesday loss to Penn State.
The Spartans (22-7, 11-5), meanwhile, tumbled to their third straight defeat despite 17 points and 12 rebounds from Adreian Payne.
Gary Harris donated 16 points in the loss, which also allowed top-ranked Indiana to claim at least a share of the Big Ten regular-season title.
Florida bear attack: Black bear mauls woman's face
Man spent 15 hours in jail for plugging electric car into an outlet at a school