Trey Burke scored 16 and Tim Hardaway Jr. had 14 in the win, which was John Beilein's 100th coaching victory at Michigan (9-0).
Marshawn Powell led Arkansas (4-4) with 18 points. Kikko Haydar scored 13.
Michigan led 42-32 at the half, but Arkansas cut the lead to 56-55 on Rickey Scott's layup with 8:48 to play in the second half.
Michigan then hit two unanswered 3-pointers and pulled away.