Appling's layup with 41.5 seconds left put the Spartans (16-3, 5-1 Big Ten) ahead to stay at 55-53 and his slam dunk off an assist from Branden Dawson with 18 seconds to go sealed the victory.
Adreian Payne supplied 14 points, while Dawson finished with nine points and 10 rebounds as Michigan State improved to 12-0 at home.
The Buckeyes (13-4, 3-2) got six 3-pointers and 28 points overall from Deshaun Thomas, but it wasn't enough to preserve their two-game winning streak.
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