Tanner Pearson and Dustin Brown also scored for Los Angeles, which has alternated wins and losses over its past nine games. The Kings pulled into a tie with Anaheim for third place in the Pacific Division with 86 points, and hold the tiebreaker over the Ducks.
Jonathan Quick made 24 saves for the Kings, who appeared headed to a second straight loss until Brown tipped home a point shot from Drew Doughty with 46.5 seconds left in regulation. Doughty finished with three assists.
Joel Eriksson Ek scored for the first time in 13 games with 2:31 left to give Minnesota the lead after trailing 2-0.
Eric Staal added his 39th and Zach Parise had his second goal in three games for the Wild. Devan Dubnyk stopped 26 shots for Minnesota, which is in third in the Central Division, four points ahead of Colorado.
Pearson opened the scoring before the end of the first period with his 15 goal of the year after Dustin Brown's quick no-look pass back to Pearson for a quick one-timer with 1:13 left in the period.
Los Angeles added a power-play goal in the second by Jeff Carter. Jake Muzzin's shot from the point deflected off Minnesota's Mikko Koivu, slowing the puck down and bouncing to Carter, who had an open net to the right of Dubnyk.
Carter has seven goals and two assists in 12 games since returning from surgery to repair a tendon in his ankle.
The two-goal deficit ignited the Wild, who pressured and scored their first goal about six minutes later as Parise brought the puck in the zone and skated across the front and snapping a wrist shot past Quick.
Minnesota added its own late-period goal to end the second when Staal scored his 13th goal in the past 14 games. Ryan Suter sent Staal into the zone on a long pass and Staal's quick shot flew past Quick's right shoulder with 56 seconds left.
NOTES: Los Angeles F Trevor Lewis left the game with an upper body injury and did not return. ... Kings D Derek Forbort left the game in the first after he was cut near his ear by Zach Parise's skate but did return in the second. ... Per the Elias Sports Bureau, Staal could join Gordie Howe as the only players in NHL history with at least nine seasons between 40-goal campaigns. Staal has his most since scoring 40 in 2008-09. ... Los Angeles C Alex Iafallo was scratched for the first time since Jan. 4, a span of 32 games. Andy Andreoff was in the lineup after being scratched 11 games in a row. ... Minnesota got three assists from its defensemen. Wild defenseman have now accounted for 36 goals and 142 assists this season. Their 178 points from the blue line is second only to Nashville's 181 this season.
Kings: At Winnipeg on Tuesday night.
Wild: Are off until hosting Nashville on Saturday.
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ST. PAUL, Minn. (AP) - Jeff Carter scored his second goal of the game with 33.8 seconds left on the clock in overtime and the Los Angeles Kings recovered after giving up a two-goal lead to beat the Minnesota Wild 4-3 on Monday night.