Stauskas drained four 3-pointers, while Burke added five assists for Michigan (7-0), which triumphed in its first true road game of the season.
Jordan Morgan added a double-double of 10 points and 10 rebounds for the Wolverines. Michigan's leading scorer, Tim Hardaway Jr., was held to just nine points.
Bradley (5-2) was led by Walt Lemon Jr. with 15 points. Tyshon Pickett, Will Egolf, Jordan Prosser and Jalen Crawford also reached double figures in scoring for the Braves.