SAINT PAUL, Minn. -- A return to home ice did little to spark the slumping Minnesota Wild on Tuesday.

Defenseman John Klingberg scored in overtime as the Dallas Stars won for the fourth time in five games, beating Minnesota 4-3.

Defensemen Alex Goligoski and Jason Demers and right winger Patrick Eaves also scored for the Stars, who won four of their last five. Goalie Kari Lehtonen, starting for the first time since Jan. 19, had 37 saves in the win.

"Kari was fantastic, he made some really good saves for us that allowed us to get to overtime," Dallas coach Lindy Ruff said. "He needed a game like that. 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 because to this point, he's had a little bit of a struggle going through January."

Minnesota followed a disappointingly familiar script while falling to 1-9-2 in its past dozen games.

The Wild started strong, then faded. First-period goals by center Erik Haula and right winger Justin Fontaine and a power-play goal in the third by center Mikko Koivu gave the Wild a chance, but they remain winless at home in 2016. Minnesota fell to 1-10 in overtime this season as goaltender Darcy Kuemper had 26 saves in the loss.

Klingberg's winner came on a wrist shot from 15 feet out, beating Kuemper on the glove side.

"He's done it a few times in overtime now," Lehtonen said in praise of Klingberg. "I think he waits out the defenders and waits out the goalies, and has that special hockey sense that few only have. That makes him very dangerous when he has time."

Koivu's tying goal came on a scramble in front of the net, with Wild defenseman Matt Dumba knocked down in the crease next to Lehtonen. The Wild captain was able to tap the loose puck over the line, and after a lengthy review, the goal stood.

The Wild dominated the third, outshooting Dallas 17-4, but could not get the go-ahead goal.

"It's very easy right now to find negatives. It is extremely easy," Wild coach Mike Yeo said. "But nothing easy is going to get us out of this. ... We're not all about moral victories. We're not all about just trying to point out the positives and deflect against what's real, but the truth of the matter is that's the only way out of this. The fight we had in the third period, that was great. That hasn't been there for us lately."

Minnesota (23-20-10) emerged from a wide-open first period with a 2-1 lead, scoring the first and last goals of the opening 20 minutes. Haula opened the scoring with his fifth goal of the season, taking a lead pass from left winger Thomas Vanek and coming in from the left of the crease. Haula skated in front of Lehtonen and lifted a backhand shot that eluded the goalie's glove and hit the upper right corner of the net.

"For the most part, we played a good game, but right now it's got to be a perfect game to win," Vanek said, as Minnesota continued its slide out of the Western Conference playoff picture.

Dallas (34-15-5) answered five minutes later when Goligoski scored for the first time since Dec. 15. Camped out near the right circle, Goligoski got a pass from center Tyler Seguin, who was behind the net, and snapped off a low shot that slid under Kuemper to tie the game.

The Wild regained the lead shortly thereafter as a pass from Haula found Fontaine behind the Dallas defense, springing a 2-on-0 break with Wild defenseman Marco Scandella on the wing. As he approached the net with Seguin closing fast, Fontaine feinted like he might pass to Scandella, then popped a forehand shot under Lehtonen's left arm for the goal.

Dallas didn't score on an early second-period power play, but tied the game 2-2 when a short-range shot by Demers hit Wild defenseman Nate Prosser at the right of the goal and deflected past Kuemper. It was just the seventh goal of the season for Demers, but his second in the past three games. Eaves gave Dallas a 3-2 lead near the midway point of the second on a power play, blasting a slap shot past Kuemper from the right faceoff dot.

NOTES: After both were healthy scratches in Minnesota's 4-1 loss in St. Louis on Saturday, Wild LW Thomas Vanek and LW Jason Zucker were back in the lineup on Tuesday. Both are in the midst of significant offensive slumps. ... The Wild's current skid began in January, when they notably went without a home win in the month. ... Dallas had a rough first month of 2016 as well, going just 3-6-2 in January. ... The work of constructing an outdoor rink at the 50,000-seat TCF Bank Stadium in Minneapolis began this week. Minnesota hosts the Chicago Blackhawks there on the afternoon of Feb. 21, marking the first time a NHL Stadium Series game has been played in Minnesota. ... Seventeen Stars players have their fathers along on this road trip. The Dallas dads got a tour of the Minnesota Twins clubhouse at Target Field in Minneapolis on Tuesday prior to the game with the Wild. ... Minnesota, in the midst of a three-game homestand, hosts the Washington Capitals on Thursday night. ... Dallas visits the Chicago Blackhawks on Thursday to finish a two-game road swing.