Syracuse guard Scoop Jardine had 19 points and Kris Joseph added 14 points off the bench.
The Spartans (6-3) were led by guards Durrell Summers and Korie Lucious with 18 and 10 points, respectively.
Syracuse (9-0) built a 38-29 halftime lead before the Spartans rallied within 48-46.
That's when Jackson pulled down an offensive rebound and scored inside, making it 50-46. Michigan State's Draymond Green hit a free throw, making it 50-47 with 12:24 remaining. However, the Orange finished the game on a 22-11 run.
The victory was Syracuse's fourth consecutive against the Spartans.
Michigan State's loss was its third this season to teams currently ranked in the Top 10. Earlier this year, the Spartans lost to UConn 70-67 and at No. 1 Duke 84-79.