Koivu scored his seventh goal and added two assists for the Wild, who opened up a home-and-home series by beating the Calgary Flames 3-1 victory on Saturday night.
The Wild had lost seven of nine (2-5-2) before Saturday and dropped to 14th in the Western Conference. Minnesota, which jumped over Calgary into 13th with the win, will host its Northwest Division rival Monday.
"When you're struggling a little bit it's hard on everyone," said Koivu, who matched a season high with three points. "You have to find a way to come out of it. You have to work as hard as you can and just believe in yourself."
Koivu had a big night one day after Wild coach Todd Richards had a one-on-one meeting with him.
"Mikko was tremendous in the game. He was great. He stepped up, and the rest of the team followed," Richards said. "I truly believe that teams follow their leaders. We have other leaders on the team, but when you're wearing the 'C,' that's one of the responsibilities. The team takes on your personality, takes on how you play the game."
Koivu has 28 points this season. Last season he had a team-high 71.
Matt Stajan had the only goal for the Flames.
"We blocked a lot of shots," Koivu said. "The 'D' did a very good job of keeping their guys away from the front of the net and letting Backstrom see the pucks. Obviously, that's huge. They're a big team and they come to the net hard, and we knew that. It's a big challenge for the 'D' and they did a very good job."
Calgary captain Jarome Iginla failed to earn a point, ending his streak at nine games. He had five goals and seven assists during the run, that was the second-longest active streak behind a 20-game spurt by Pittsburgh's Sidney Crosby.
"We knew the importance of the game. They did, too," Iginla said. "They were coming off two losses. They were a very desperate team. It's not like we gave them a million chances. They were opportunistic. They got a power-play goal, and we didn't capitalize on our chances. In a tight game, that was the difference."
Minnesota took advantage of its first power play when Koivu sent a cross-ice pass to Miettinen, who one-timed a shot past goalie Miikka Kiprusoff.
The goal came after an uneventful first half of the game that included a 10-minute stretch of listless play in which the teams combined for one shot.
Minnesota increased its lead to 2-0 in the final minute of the second. Koivu redirected the puck past Kiprusoff after Wild defenseman Brent Burns sent a low shot toward the front of the net. Andrew Brunette sparked the play with a clever pass to Burns and earned the second assist at 19:07.
"We were trying to get something going, and that killed our momentum," Flames defenseman Cory Sarich said.
Stajan broke Backstrom's shutout bid at 14:43 of the third period with his second goal in 45 games, dating to last season.
"We didn't play the whole game like we played the last eight or nine minutes," said Stajan, who had no goals in 18 games. "If we played like that the whole game, there's not doubt how that game would have turned out."
Backstrom, who had allowed 28 goals in his previous six starts, looked sharp. His biggest stop was a glove save off Alex Tanguay early in the second on a sharp-angled one-timer.
The Flames were 0 for 1 on the power play. ... It was the first time since Oct. 19 that the Wild scored more than one goal in the second period. ... Minnesota C Matt Cullen (groin) returned after missing three games. D Cam Barker sat out because of personal reasons. ... Flames LW Curtis Glencross was a healthy scratch for the second straight game. ... Iginla's 31 career goals against the Wild are the most of any opponent, 13 more than Milan Hejduk and Daymond Langkow, who are next on the list. Calgary is 18-2-1 against Minnesota when Iginla scores.