Parise and Cullen also scored in the shootout for the Wild.
Minnesota is 10-2-0 in its past 12 games and moved into first place in the Northwest Division. Maybe more impressive, though, was the Wild rallying from two goals down one night after having their seven-game win streak end in Dallas.
"All I can say is just huge amounts of character," Wild coach Mike Yeo said. "It's back-to-back games, they're sitting here waiting for us, down 3-1 against a team that doesn't give you much and you've got to fight for every inch that you get on the ice. So just a great job by our guys."
"You're up 3-1 and you give up two points. That's not what you want to do," Quick said. "We're just trying to climb the standings and trying to win games every time you're out there. You're not looking at possible playoff standings, you're just trying to climb them."
The Kings took a 3-1 lead midway through the second period when Williams scored on a breakaway after blocking Clayton Stoner's shot attempt at point-blank range. Two minutes later, though, Coyle gave the Wild a boost by scoring on a backhand from his knees after whiffing on his initial attempt.
Coyle missed badly and fell after taking a pretty pass from Parise from behind the net. He more than made up for it by sneaking his second attempt under Quick's stick to make it 3-2.
Then Parise tied it in the third just as L.A. killed off a 5-on-3 Minnesota power play. The crowd just finished booing the Wild for failing to get a shot during the two-man advantage when Koivu went cross ice to find Parise, who wristed it past quick from the left circle to make it 3-all.
"It was a sloppy game from us," Williams said. "That's certainly not the way we intended to play the game, but somewhere along the way we lost our way and let a team back in a game we had full control of."
While the Kings weren't thrilled with their performance -- coach Darryl Sutter left without speaking to the reporters -- the Wild were more than happy to praise the defending champs.
"I think that's probably the best team we've played," Parise said. "I think they had a tough start, the usual Cup hangover, but they're playing really well of late, and they're dangerous. To get a win against them is really big because you know that's a team that's going to be there in the end."
Backstrom won his eighth consecutive start, a new career high, and his league-leading 19th game of the season a night after sitting out for the first time in 13 games.
L.A. led 1-0 after Brown's goal at 7:58 of the first period, but Cullen tied it at 13:19 after a turnover.
The Kings have scored two power-play goals on the road four times this season, but have lost all four games. ... Wild C Torrey Mitchell was scratched due to an illness. ... Cullen has 19 points in his past 19 games, and Devin Setoguchi has 10 points in his past 10.
Copyright by STATS LLC and The Associated Press
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