Harris was 5-of-9 from the field and Nix sank 7-of-10 shots in Michigan State's (21-4, 10-2 Big Ten) 10th win in their last 11 games.
Tray Burke led Michigan (21-4, 8-4) and Nik Stauskas added 10. Michigan lost for the third time in four games after exploding to a 20-1 start this season.
Michigan State led 38-24 at halftime and shot 48.4 percent from the field to 39.6 percent for their in-state rivals. They also out-rebounded the Wolverines 40-28.