The Golden Gophers (17-6, 5-5) struggled in large part because Andre Hollins, Joe Coleman and Austin Hollins combined to make just 10 of 34 shots. Appling and Harris, meanwhile, made almost half of their 21 attempts.
"That was the difference," Minnesota coach Tubby Smith said.
Appling left the court with 1:17 left, holding his right shoulder after getting tied up with Joe Coleman. He returned to the bench in the final minute, but couldn't play.
The Spartans (19-4 8-2 Big Ten) moved into a second-place tie with No. 3 Michigan, whom they host Tuesday night. They picked up their eighth win in nine games since losing the conference opener against the Gophers on the road, rallying to win a second straight game with a solid second half and playing poorly in the first half.
Minnesota has lost five of its last seven games.
"We still believe," Gophers forward Trevor Mbakwe said. "We've got five losses, but we still are going to win — and win out.
Michigan State took control of the rematch with a 21-4 run — after trailing by five points early in the second half — to take a 41-29 lead.
"We wait until we get hit in the face," Appling lamented. "And we're going to wind out getting bit in the behind."
The Spartans pulled away with some shots and stops.
Appling made a layup, Adreian Payne connected on two free throws and Harris had a three-point play to put them ahead by 11 points with 1:35 to go. Payne blocked a shot and Derrick Nix had a steal during the victory-sealing stretch.
"When you give up easy baskets and just throw the ball to the guy those are just back-breakers," Smith said. "I was disappointing we didn't handle the ball better."
The Gophers didn't have a scorer in double figures until Andre Hollins' 3-pointer with 3:38 left pulled them within five points. Andre Hollins finished with 11 points. Coleman was one of his three teammates with nine points and Austin Hollins scored eight.
"We just beat a very good basketball team," Michigan State coach Tom Izzo said. "I don't think they played great and I don't think we played great."
A fired-up crowd got quiet when Appling left the game in another potential setback for a banged-up team and roared when he jogged back to the bench with 40 seconds left in the game.
Travis Trice, Appling's backup, wasn't cleared after having a head injury last week. Harris played after being knocked out of the previous game with back spasms and was limited in practice early in the week.
The Spartans also lack depth in the backcourt because Brandan Kearney transferred during the season to Arizona State.
Payne was out of the game for part of the second half with a bloody nose.
The Spartans had much more success offensively with their guards shooting from the outside on a night their post players struggled. They made 9 of 18 3-pointers and connected on fewer than 44 percent of their shots overall.
Nix and Payne, both averaging nine-plus points, each missed all three of their shots and were scoreless in the first half.
Nix made the opening shot of the second half, tying the game at 20 after each team struggled to shoot in the first half. Payne had 11 points in the second half to help Michigan State maintain its dominance against the Golden Gophers.
The Spartans have beaten Minnesota in 13 of the past 15 games overall and 14 straight at the Breslin Center, where they're undefeated this season. That mark will be tested next week against the rival Wolverines and the following week against top-ranked Indiana.
Minnesota returns home to play Illinois and Wisconsin over the next week and Mbakwe said his teammates have to keep playing tough.
"The Big Ten is physical," he said. "You get fouled pretty hard, but it's part of the game. You just have to play through it."