Los Angeles won for the fifth time in six games and Quick stopped 20 shots.
"The start wasn't the best there," Kopitar said. "But it doesn't matter, two points are two points at the end of the day. Too bad it came in a shootout and not in regulation, but whatever it is, we'll take the two points."
Los Angeles' Dustin Brown -- the Kings' leading goal scorer -- was given a major penalty and a game misconduct after a blow to the head of Miettinen in the second period. Miettinen was attempting a shot in the slot when Brown came through, lowering his shoulder and connecting with Miettinen's head and shoulder.
"Brownie actually comes around in front of the player and hits shoulder on shoulder," Los Angeles coach Terry Murray said. "There was no blow to the head. You have an offensive player in a prime scoring area shooting the puck."
"There was not, in my view on the replay, a blindside hit."
Minnesota put four shots on goal on the ensuing five-minute advantage, but came up empty. After scoring 12 times on their first 27 power-play opportunities this season, the Wild are 0 for 8 in their past two games.
"Power plays are up and down," Minnesota center Matt Cullen said. "It's a long season. Certainly we want to be better than we have the last two games. We have it in here. It's just a matter of getting back to executing, getting more pucks to the net."
The Kings' penalty killing allowed time for the offense to find its rhythm and the Wild provided Los Angeles plenty of power-play opportunities.
Stoll connected for his third of the season on the power play near the end of first period.
Kopitar scored on a 5-on-3 advantage with 18 seconds remaining in the second.
With less than two minutes remaining in the second, the Kings had an open net as Backstrom tripped after colliding with defenseman Marek Zidlicky. As Ryan Smyth fired the shot, Guillaume Latendresse slid across and managed to deflect Smyth's shot.
However, Los Angeles scored on its next chance. Mikko Koivu was assessed a hooking penalty and Kopitar scored just 6 seconds into the two-man advantage, firing a rebound past Backstrom.
"They put us on our heels," Minnesota coach Todd Richards said. "The first two penalty kills I thought we did a pretty good job as far as killing the power-play opportunities, but you can't keep giving a good team opportunities."
The Kings entered the game just 3 for 27 on the power play this season, but converted two of their seven chances against Minnesota. Los Angeles was seventh in the league on the power play last season, converting 20.8 percent of its chances.
"The part that has been troubling for us has been recovering pucks and having a shot mentality," Murray said. "I thought we started to get more to that tonight. When you get a 5-on-3, I wish we did in 5-on-4s what we did in 5-on-3, an automatic shot, there is no hesitation on it."
Los Angeles D Drew Doughty missed his third straight game with an apparent concussion after being put on injured reserve earlier Monday. Doughty -- who has been skating at the team's training complex -- is eligible to return Thursday, but isn't expected back before Saturday when the Kings return from their current five-game road trip. Rookie D Jake Muzzin was recalled from Los Angeles' AHL affiliate in Manchester. ... Minnesota C Pierre-Marc Bouchard took another step toward his recovery from a concussion by particapating in contact drills during practice. Bouchard took a hit to the head in March 2009 and hasn't played since the opener last season. ... Minnesota D Cam Barker missed his second straight game with a groin injury. Clayton Stoner was in the lineup in place of Barker and recorded his first point of the season with a first-period assist. ... Stoll has six points with three goals in his past six games. Kopitar has seven points in his last seven games.