The disappointing Wolverines (5-4) pulled away in the final minutes after trailing at halftime to avoid a losing record after starting the season No. 15 in The Associated Press poll. Their next game is Saturday at No. 1 Kansas.
Michigan has started poorly after being ranked in the preseason for the first time since 1996, following its first NCAA tournament bid in more than a decade.
Detroit had a chance to match its win total from last year in coach Ray McCallum's debut season.