The Spartans, the last of the No. 1 seeds to play in this year's event, moved into the third round of the West Region and will face St. Louis Sunday.
Green scored 24 points, claimed 12 rebounds and handed out 10 assists. The Spartans scored 45 points over the final 18 minutes after holding only a five-point advantage at halftime.
Adreian Payne added 16 points and seven rebounds and Keith Appling had 10 for Michigan State (28-7), regular-season and tournament champion of the Big Ten Conference.
Although the tournament saw the unprecedented upsets of two No. 2 seeds Friday, this year's tourney extended the unbeaten streak of No. 1s to 112 over the 28 years the current seeding format has been in place. Syracuse, Kentucky and North Carolina also won as a No. 1 seed this year.
Long Island (25-9), a regular-season and tournament titleholder out of the Northeast Conference, was led by 17 points from Jamal Olasewere.