Michigan State remained unbeaten in its 15 home contests this season and pulled within a game of Ohio State for the lead in the Big Ten Conference.
The Spartans scored the game's first nine points, led by 13 at the half and built the advantage to 22 early in the second period. Penn State then closed its deficit to only five with 9:51 to go before Michigan State began to pull away again.
Green added 12 rebounds while Branden Dawson and Adreian Payne both had 12 points for the Spartans (19-5, 8-3 Big Ten).
Penn State shot just 38 percent and made only 14 field goals from 2-point range. The Nittany Lions managed six from beyond the arc.
Tim Frazier led Penn State (10-15, 2-10) with 19 points. The Nittany Lions are in the Big Ten cellar.