Zeller connected on 7-of-12 shots en route to 18 points. Victor Olapido added 13 and Verdell Jones III put in 12 for the Hoosiers (23-7, 10-7 Big Ten), who logged their third straight win.
Christian Watford contributed 10 points and 14 rebounds, and Jordan Hulls added 10 points as Indiana improved to 17-1 at home with a third victory over a Top-5 team this season.
Draymond Green poured in 29 points on 10-of-17 shooting for the Spartans (24-6, 13-4), who saw their seven-game winning streak snapped.
MSU, which has already clinched a share of the Big Ten title, blew a chance to win the conference crown outright.