ST. PAUL — Kari Lehtonen needed a game like this in goal for the Dallas Stars.

Far more desperate for some success to savor, the Minnesota Wild simply found more of the same.

John Klingberg scored in overtime and Lehtonen made 37 saves to win for the first time in more than a month, giving the Stars a 4-3 victory Tuesday and sticking the Wild with their 11th loss in the last 12 games.

Lehtonen started for the first time in the last seven games.

“I wanted him to feel good about himself, and after that game if he can build off that, it’s a huge step in the right direction,” Stars coach Lindy Ruff said.

Jamie Benn, who had two assists, set up Klingberg’s high shot from the slot that eluded Darcy Kuemper with 2:21 remaining in the extra period.

“I had a lot of time to aim where I wanted to shoot,” Klingberg said, “so I was trying to go high and it was nice to see it go in.”

Patrick Eaves added a goal and an assist and Tyler Seguin notched two assists for the Stars, who recovered well from a 5-1 loss Saturday at Chicago.

“It was fun. I was excited all day to get out there and play for the first time in a long time, and I’m glad it went well,” said Lehtonen, who stopped 16 of 17 shots by the Wild in the third period.

Mikko Koivu’s power-play goal evened the game just 76 seconds after the second intermission, finishing a chaotic sequence in front of the net after Zach Parise and Matt Dumba each hit the post with their shots. Dumba was taken down by Stars defenseman Johnny Oduya, and as he laid face-first in the crease with his stick in the net, Koivu punched in the puck without it hitting Dumba’s hand. Replay review upheld the goal, and Ruff didn’t challenge the ruling.

But the Wild couldn’t get any more pucks past Lehtonen, and they fell to a woeful 1-10 in the 3-on-3 overtime format this season.

“If things are going reasonably well, that’s a game you probably, despite only getting one point, still feel reasonably good about,” Wild coach Mike Yeo said. “But that’s pretty tough right now.”

Erik Haula and Justin Fontaine scored on breakaways for the Wild in the first period for the strong start they needed, but Minnesota native Alex Goligoski gave the Stars a goal between them off a slick behind-the-net pass from Seguin.

Jason Demers tied the game at 2 early in the second period with a going-wide shot that glanced off Wild defenseman Nate Prosser and slipped past Kuemper, fittingly for how rough the new year has been for the home team. Then, Eaves put the Stars in front with his power-play shot set up by another fine feed from Seguin.

“Everyone keeps saying it’s going to be hard to get out of this, and it really is,” Haula said. “It wasn’t enough again. We weren’t good enough.”

The Wild stumbled home for their first game at Xcel Energy Center in 15 days. Thomas Vanek, who had two assists, was back on the third line after being a healthy scratch Saturday at St. Louis. Jason Zucker returned to the fourth line from the same punishment, but the Wild were without two of their top defensemen, Jonas Brodin and Jared Spurgeon.

That’s a difficult way to play the NHL’s second-highest-scoring team, with an average of 3.2 goals per game and two of the top four scorers in the league with Benn and Seguin. Jason Spezza missed his second straight game with an upper-body injury, but the Stars had more than enough juice to overcome his absence.

“For the most part, we played a good game, but right now it’s got to be a perfect game to win,” Vanek said.

NOTES: Brodin, on injured reserve with a broken foot expected to keep him out until sometime in March, missed his second straight game. Spurgeon sat out with a less-serious injury the team called a bone bruise. … The Stars won four of five games against the Wild this season, three in overtime. … Goligoski scored for the first time in 23 games since Dec. 15. … The Wild are 0-3-3 in their last six home games and haven’t won here since Dec. 28 against Detroit.