The Spartans, who won their second straight after losing two in a row, maintained a comfortable second-half lead while shooting 54 percent from the field.
Green hit 9-of-11 of his shots and Branden Dawson added 16 for the Spartans (17-4, 6-2 Big Ten Conference). Michigan State is in a three-way tie with Michigan and Ohio State for the top spot in the league race.
Rodney Williams led Minnesota (15-6, 3-5) with 15 points. The Golden Gophers had won three in a row.