The Wild, playing their fifth game in eight days, rallied from a 3-1 deficit to tie the game near the midway point of the third period.
"We battled for 65 minutes and came out with a shutout win," Brett Clark said. "Everybody's coming together, there's no quit. No matter what happens on the ice, this team knows we have a chance to win. It doesn't matter if we are down by two or up by three. This team in here, everyone of us, believes we can win every night."
The Wild (21-11-2) scored on all three shootout attempts and Niklas Backstrom stopped one of two to complete the comeback.
The Kings (19-12-3) took its two-goal lead at the 11:24 mark of the second period when Justin Williams blocked shot and raced up ice for a breakaway goal.
Charlie Coyle started the rally for the Wild by sliding a puck under a diving Jonathan Quick from his knees into the net at the 13:53 mark of the second period.
Zach Parise tied the game with 11 minutes and 54 seconds remaining in regulation, seconds after the completion of a 59-second 5-on-3 advantage. The backdoor feed from Mikko Koivu extends Parise's team lead in goals to 15.
"We had a little trouble getting it setup and getting it in, but when we did, we had some good looks," Parise said.
Clark made his Wild debut and 25 shifts for 15 minutes and eight seconds of ice time. The 36-year-old was signed to provide depth on the blue line, but has found it harder and harder to get in the lineup as the Wild rattled off seven straight wins before losing Friday in Dallas.
"The group of guys we have around here made it pretty easy to get out there," he said. "The adrenaline was running in the first period. I was a little aggressive on a couple plays, but I settled down. I had a blast out there."
The Wild have a day off before facing the St. Louis Blues Monday at the Xcel Energy Center.
Torrey Mitchell was scratched before the game with an illness. He was replaced on the fourth line by defenseman Nate Prosser…Ryan Suter recorded his team-leading 25th assist, which tied him for the league lead in assists and points by a defenseman this season…The Wild improved to 4-1 in shootouts this season…The Wild tied a franchise record for wins in a single month with 11, previously done Nov. 2011…Niklas Backstrom won his eighth straight start, a career-high.
No. 3 – Justin Williams. The Kings forward scored a goal.
No. 2 – Mikko Koivu. The Wild forward recorded two assists and scored the shootout determining goal.
No. 1 – Zach Parise. The Wild forward recorded a goal and an assist.
Los Angeles…..1 2 0 0 – 3
Minnesota…….1 1 1 0 – 4
First Period – 1, Los Angeles, Brown 14 (Muzzin, Kopitar), 7:58 (pp). 2, Minnesota, Cullen 7 (Setoguchi, Bouchard), 13:19. Penalties – Stoner, Min (holding), 6:55; Martinez, LA (holding), 19:38.
Second Period – 3, Los Angeles, Carter 19 (Doughty, Toffoli), 3:44. 4, Los Angeles, Williams 6 (unassisted), 11:24. 5, Minnesota, Coyle 4 (Koivu, Parise), 13:53. Penalties – Clutterbuck, Min (interference), 3:05; Quick, LA (tripping; served by Martinez), 17:25.
Third Period – 6, Minnesota, Parise 15 (Koivu, Suter), 8:06 (pp). Penalties – Nolan, LA (goaltender interference), 6:03 Stoll, LA (hooking), 7:05.
Overtime – None. Penalties – None.
Shootout – Los Angeles Brown (save), Richards (goal). Minnesota Parise (goal), Koivu (goal), Cullen (goal).
Shots on goal – Los Angeles 13-10-7-1 31. Minnesota 11-7-7-3 28.
Goalies – Los Angeles, Quick (25-28). Minnesota, Backstrom (28-31). A – 19,223. Referees – Eric Furlatt, Mike Hasenfratz. Linesmen – Matt MacPherson, Jay Sharrers.