Shortly before the game, Wild coaches adjusted the team's power play to have the defensemen go wider, a move to produce more shots from the point and open things up more.
The Wild, 1-for-21 with a man advantage in their previous five games, finished 4-for-7.
"We didn't even practice it. I guess sometimes when the players don't know what they're doing it works," Belanger said. "It's really hard in this league to score goals five-on-five. The system and everything is really good. It's hard to get some chances close to the net, the goaltenders are so great. Your power play is going to get you a lot of goals. It got us going."
Backstrom, who beat Tampa Bay 1-0 on Oct. 18, is 8-0 against the Coyotes with a 1.13 goals-against average and three shutouts.
Phoenix, which had won three straight, was shut out for the second time in five games.
"It was a good old fashioned butt-kicking," Phoenix coach Wayne Gretzky said. "They played as a team. We played as individuals. They deserved to beat us. They outskated us at each end of the ice."
The Coyotes rarely tested Backstrom because the Wild defense kept them away from the crease. Phoenix often settled for wrist shots from above the dots and failed to get to rebounds.
"It was probably one of the best games for us this season for 60 minutes," Backstrom said. "We didn't give them anything. Our PK was really strong today. We took a lot of penalties, but we killed them. I think that's the sign of a good team."
Phoenix was 0-for-6 on the power play and is 2-for-28 in its past five games.
After a scoreless first period, Minnesota scored two power-goals in the second.
A one-timer from Zidlicky in the high slot beat Ilya Bryzgalov on the stick side during a two-man advantage early in the period. It was his first goal in 29 games. Afterward he pointed to his wife, Karina, who saw her first Wild home game.
"I've been here without her for two months so it was exciting," said Zidlicky, acquired from Nashville last summer.
Brunette's goal came 12 minutes later when he took a touch pass from Zidlicky in the left circle and beat Bryzgalov with a wrist shot.
Bryzgalov is 0-6 against Minnesota yet was praised by Gretzky for not letting the game get more out of hand.
"Four-nothing is flattery," he said. "If it wasn't for Bryzgalov it would've been 8-0."
Zidlicky's five-on-three goal was set up when Brent Burns took a slash from Garth Murray as he closed in on the Phoenix net.
In his return after a four-game absence due to an upper body injury, Burns -- a defenseman -- moved up to play with Brunette and Belanger in try to add offensive punch to a Wild lineup that had eight goals in five games. Minnesota coach Jacques Lemaire said he'll likely keep Burns on the wing.
Owen Nolan also returned to the Minnesota lineup after missing five games with an upper body injury. He skated with Pierre-Marc Bouchard and Mikko Koivu, finishing with two assists. Nolan just missed on a first-period tip, and his rebound attempt was just wide as he tried to lift a backhander over the fallen Bryzgalov in the second period.
Marian Gaborik missed his 12th straight game with a lower body injury. There is no timetable for his return.
"It was the first time that I feel good behind the bench having pretty much all the guys back, and still our top guy is not there," Lemaire said.
"When Burns will be on top of his game, that line's going to be a lot better. Nolan played fine but missed three goals. When these guys start to get hot and start to score it'll be good for our offense," he said.
Belanger scored early in the third, converting a perfect cross-crease pass from Nolan. Zidlicky beat Bryzgalov with a slap shot with 1:07 to play.
"It comes down to the power play," Phoenix captain Shane Doan said. "We had some opportunities. They capitalized on theirs and we didn't on ours. That was the difference in the hockey game."
Backstrom is 43-0-3 when leading after two periods. ... To make room for Nolan, Krys Kolanos was reassigned to AHL Houston. Kolanos had one goal in two games following his Nov. 3 recall. ... Phoenix defenseman Derek Morris played his 200th consecutive game.