Coming off its win over top-ranked Kentucky, the Spartans found themselves in a tough fight with the Lions.
Columbia trailed by only one with 4:15 to play after Alex Rosenberg hit a layup, but the Lions did not score another point. Payne started the eight-point, game-ending surge with a free throw, scored on a dunk with 1:19 to go and closed the scoring with two foul shots.
Payne finished with 26 points and 11 rebounds while Gary Harris had 11 for the Spartans (3-0). Michigan State attempted seven 3-point shots and missed them all.
Columbia (1-2) was led by Maodo Lo with 12 points.