Cook was perfect in 10 trips to the foul line and also handed out nine assists for Duke (7-2), who won their 107th consecutive home game against a non-conference opponent.
Jabari Parker chipped in 15 for the Blue Devils and Rodney Hood scored 14. Duke led 32-22 at halftime and played an even 47-47 with Michigan in the second half.
Caris Levart led Michigan (5-3) with 24 points. Mitch McGary notched 15 points and 14 rebounds. The Wolverines were largely without primary scorer Nik Stauskas, who sat out Michigan's last game with an ankle injury and scored only four points Tuesday, all from the free-throw line.