Chad Johnson withstood an early barrage by Minnesota and stayed steady all night for Calgary in the net.
Johnny Gaudreau took some hard hits and left the game twice after scoring the only goal.
Troy Brouwer found two teeth in his mouthguard.
That's the kind of gritty game this was. That's the kind of grinding victory the Flames badly needed.
Gaudreau's goal early in the first period held up and Johnson stopped 27 shots for Calgary's first shutout of the season, fueling a 1-0 victory for the Flames over the Wild that ended their four-game losing streak on Tuesday.
"It's almost more confidence-building for us than like a 7-5 game or something," Brouwer said. "To be able to hold the lead all the way to the end, get Johnny a shutout, those are huge things that guys really take pride in. So tonight the way we won is just as important as the win itself."
Outscored 17-4 over the skid, with two of those goals from Gaudreau, Johnson and the Flames gave their NHL-worst goals against average a big boost. Their scoring differential, now at minus-19, is last in the league. Flames goalie Brian Elliott, formerly of the St. Louis Blues, has an 8-2 record with a 2.18 goals against average in 12 career games against the Wild, but Johnson got the call from coach Glen Gulutzan instead.
"We got better as a group as the game went on, and everybody was more confident defensively," Johnson said. "They had a little bit of pressure and we weathered the storm, and you could see that we didn't get rattled with them coming hard at us."
Devan Dubnyk made 26 saves and has given up only nine goals in his last eight games, stopping 245 of 254 shots, but the Wild played an undisciplined game and took eight penalties for a total of 19 minutes.
"The guys are exerting all their energy to kill penalties, not to be able to score goals," coach Bruce Boudreau said. "Not making excuses for us not scoring, but that's a byproduct of that."
The Wild brought the NHL's fifth-best penalty kill at 88.1 percent into the game, but Gaudreau tallied the sixth power play goal against them this season just 6:05 into the game. Johnny Hockey made a slick move worthy of his intrepid nickname, snagging a lead pass from Mark Giordano and skating across the front of the goal mouth to get Dubnyk to go with him before tucking in a backhander for the lead.
That came just seconds after Mikko Koivu misfired on a breakaway shot. Jason Zucker and Mike Reilly each hit posts later in the game for the Wild, whose stretch of 10 games in 17 days didn't start smoothly.
"This is how we're going to have to win," Gulutzan said.
The game devolved into a slog of penalties and scuffles throughout the second period, spilling over into the third, and the Wild weren't able to knock any shots past Johnson despite myriad scoring opportunities. They've allowed an NHL-low 29 goals in 15 games.
The Flames, who didn't specify Gaudreau's injury, took issue with some slashing of their young left wing that went on, though Brouwer acknowledged that's the same way he and his teammates play against stars on other teams. Both teams had complaints about the officiating.
"We killed the whole second period," center Eric Staal said. "It just kills the flow."
The Wild fell to 4-2 at home after their first contest at Xcel Energy Center in two weeks.
"We've got to as a group ask ourselves, 'Did we really do enough to give ourselves a chance to create offense, to sustain offense, to get scoring chances?,' and I don't think we did," left wing Zach Parise said.
NOTES: Johnson's last shutout was Dec. 17, 2015, against Anaheim. ... The Wild made rookie Joel Eriksson Ek a healthy scratch for the second straight game. Eriksson Ek, who has two goals and three assists in nine games, could be sent back to his native Sweden for more playing time toward his development. ... The Wild got Parise back in the lineup after a six-game absence due to a lower-body injury. He played on the third line with Erik Haula and Jason Pominville ... For the Flames, LW Matthew Tkachuk returned from a wrist injury that kept him out for the last two games and joined Mikael Backlund and Michael Frolik on the second line.
Calgary returns home to face Arizona on Wednesday night.
Minnesota hosts Boston on Thursday night.