The Spartans produced just 18 points in the first half, shot 28 percent and trailed by two at the break before storming back to move within a half game of Big Ten Conference leader Indiana.
Michigan State held the Golden Gophers scoreless for 5:30 early in the second period while building a 12-point advantage and then held off a Minnesota comeback bid.
Harris scored 18 points and Appling had 14 while the Spartans warmed up to hit 44 percent of their field goal attempts for the game and make 9-of-17 from 3-point range.
Michigan State improved to 19-4 and is 8-2 in league play.
Andre Hollins, with 11 points, was the only player in double figures for Minnesota (17-6, 5-5).