Burke, a native of Columbus, Ohio, sank a 3-point shot just after the tip in overtime that gave the Wolverines (21-2, 8-2 Big Ten) the lead for good.
Michigan only scored four points in OT, but the Buckeyes (17-5, 7-3) only scored two on a layup by Aaron Craft with 57 seconds to play in the extra session.
Deshaun Thomas scored 17 and LaQuinton Ross 16 for Ohio State. The Buckeyes shot 51.7 percent from the field and out-rebounded Michigan 28-27 in a contest that was as close on the stats sheet as it was on the court.
Celebrity Families of 2014 [PHOTOS]