Derrick Nix donated 12 points for the Spartans, who improved to 16-0 at home this season.
Ryan Evans tallied 17 points and seven boards for the Badgers (19-7, 8-5), who have lost two of three. Jordan Taylor and Jared Berggren added 13 and 10 points, respectively.
Evans made two free throws and a jumper to give Wisconsin a 12-8 lead with 9:51 left in the first half.
But Michigan State responded with a 14-0 run to take control of the game. Green tallied seven points during the burst, which Appling capped with a three-point play to make it 22-12 with 5:24 remaining.
The Spartans used a 7-0 spurt moments later to extend their margin. Appling bookended the flurry with a layup and slam to give the home team a 31-17 edge.
Taylor's jumper cut the gap to 31-19 at the break.
Michigan State continued to dominate in the second half and held a 58-37 margin with seven minutes to play.
The Badgers tried to get back in the game with a 14-2 run. Rob Wilson and Evans each made three-pointers during the surge to help get Wisconsin within nine, 60-51, with 3:14 left.
Michigan State went 9-for-12 from the foul line down the stretch to seal the victory.