Green drained a 3-pointer with 1:35 to play after the Spartans (27-7) had gone nearly 4 minutes without scoring and Michigan State fended off a late charge by Ohio State (27-7).
Brandon Wood led the Spartans with 21 points and Derrick Nix added 10.
The Buckeyes, who had won the past two Big Ten titles, were led by Jared Sullinger, who scored 18 points and had nine rebounds. Aaron Craft contributed 10 points.
Ohio State won the rebounding battle 35-27 but shot 39.7 percent from the field and had 10 turnovers in the game.
Scarlett Johansson steps out with fiance after pregnancy reveal
Susan Sarandon 'very excited' about daughter's pregnancy