The Wolverines (9-7, 3-2 Big Ten) needed the victory after blowing a 17-point lead in their previous game against Northwestern and before hosting No. 15 Connecticut on Sunday.
Christian Watford scored 16 for the Hoosiers (7-9, 1-3) but didn't get much help. No other Indiana player scored more than seven points.
Indiana's young team was competitive for most of the game and was within 48-43 with 5:54 remaining before Michigan finished the game on a 21-2 run.
Harris had 17 of the Wolverines' 23 points during one dominant stretch in the second half.