Harris played after being knocked out of the previous game with back spasms and was limited in practice early in the week.
"Gary hit a couple big shots, the guy has ice in his veins and is tougher than nails," Spartans coach Tom Izzo said. "He could barely go. It was one of the guttier performances in my career."
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 because of his shoulder injury.
"It popped out, then went right back in," Appling said.
The Spartans lack depth in the backcourt because Travis Trice, Appling's backup, hasn't been cleared after following a head injury last week. Their frontcourt took a hit when Adreian Payne got elbowed in the face, and left the court with a bloody nose for part of the second half, while Branden Dawson was slowed by a sprained right ankle.
"I might have to play a little different with three games in six days," Izzo said.
The Spartans (19-4 8-2 Big Ten) moved into a second-place tie with No. 3 Michigan, which visits East Lansing on Tuesday night after playing Saturday night at Purdue. They picked up their eighth win in nine games since losing the conference opener against the Golden Gophers on the road.
Minnesota (17-6, 5-5), meanwhile, 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.
The Gophers didn't have a scorer in double figures until Austin Hollins' 3-pointer with 3:38 left got them within five. Hollins finished with 11 points. Coleman was one of his three teammates with nine points.
Minnesota's three-guard lineup combined to make just 10 of 34 shots. Appling and Harris made almost half of their 21 attempts.
"That was the difference," Minnesota coach Tubby Smith said.
The Spartans pulled away late in the game with some shots and stops.
Appling made a layup, 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 key stretch.
A fired-up crowd got quiet when Appling left the game in another potential setback for a short-handed team and roared when he jogged back to the bench with 40 seconds left.
"I'm hoping and thinking that it might've popped in so quickly it didn't hurt stretch anything," Izzo said.
Smith said Harris, who made 5 of 11 shots, including four 3-pointers, took advantage of poor defense.
"We found a way to leave him open most of the night," Smith said. "He was on target and was feeling it, obviously, especially stepping up without Trice. He shot us out of the zone every time we tried to go to it. He played extremely well and had a good all-around game and played a lot of minutes."
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.
"It's a good thing we were knocking down 3s," Harris said. "We couldn't take a loss at home."
Nix and Payne, both of whom are 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 it 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.