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LOS ANGELES -- The Los Angeles Kings have been leaving goalie Jonathan Quick very little room for error the past six weeks because of their struggles to score.

They finally got a goal 38 seconds into overtime from defenseman Drew Doughty during a goalmouth scramble Thursday night, and Quick tied a career best with his NHL-leading sixth shutout in a 1-0 victory over the Phoenix Coyotes.

Three nights earlier against Colorado, Quick was nursing a 1-0 lead when he gave up the tying goal with 5:43 left in regulation and the Kings lost in a shootout.

"It seems like it has happened frequently, but every game is different and brings its own challenges on for a goalie," said Quick, who is 6-0-2 in his last eight starts with a 1.20 goals against average and .956 save percentage. "Sometimes you're going to have to make 40 saves and sometimes you're going to have to make 18. You prepare to come in and not let in any. That's ultimately your goal, but sometimes they're going to get a few and you need your team to score some goals."

Quick made 22 saves in his 20th career shutout, his seventh by a 1-0 score. The previous one was against Dallas on Oct. 22 at Staples Center, when Jack Johnson got the only goal with 4:48 left in the third period -- enabling Quick to become the first goalie in franchise history with three consecutive shutouts.

The Kings, who came in with a league-low 87 goals, were held to fewer than three in regulation for the 18th time in 20 games. Despite averaging 33 shots on net in their last 15 contests, they have averaged only 1.7 goals during that stretch and are 3 for 53 on the power play. But they still haven't lost in regulation (5-0-3) since Darryl Sutter replaced Terry Murray as coach.

The sellout crowd of 18,118 groaned after Kings left wing Dustin Penner spun around in the right circle and took a 30-foot wrist shot that hit the left post with 5:47 left in regulation. A minute later, goalie Mike Smith robbed Dustin Brown at the doorstep after he stickhandled through the Coyotes' defense, and Smith came up big again to thwart Brad Richardson from in close with 3:41 left.

"Smith made some big saves to push it into overtime, but we were fortunate to get a goal early in overtime and get out of here with two points," Quick said. "There were times when our systems caught up with each other and not much was going on. But we outplayed them, I believe, for the majority of the game and we were creating some stuff around their net."

Doughty got a pass from Jarret Stoll, swerved around Daymond Langkow in the left circle and threw the puck toward the net. It caromed in off Phoenix defenseman Oliver Ekman-Larsson's skate while Johnson was in the crease. Referee Frederick L'Ecuyer immediately ruled it a goal, and the replay office in Toronto confirmed that it was legal.

"It should be no goal. The puck did go in the net, but it should be goalie interference," Phoenix coach Dave Tippett said. "If they don't give the goal to Johnson, then it's goalie interference. If he comes in and puts his leg in front of Mike Smith's leg so Smith can't make a stop, that is goalie interference. It's as simple as that. It's a poor call. It's a blown call that should be no goal. I think we got a bad break."

Coyotes captain Shane Doan agreed.

"The ref who made the call was more watching the net come up off the moorings and not paying attention to what's in the crease," Doan said. "Honestly, with the way their guy drives to the crease and stops Smitty from going across the net, that's a no-brainer -- you assume. But apparently, there's more concern with watching the net than watching our goalie."

In any event, it was Doughty's 10th game-winner among his 36 career goals.

"I just wanted to get into the play," Doughty said. "I saw that we had control of the puck, so I raced up to the blue line. Me and Stolly made eye contact and he made a nice pass. Then I just tried to drive the net. Sometimes you just have to score those dirty goals. It was huge. Obviously, I haven't been scoring a lot this year and I finally contributed on the score sheet with a goal for the team."

Smith made his second start after missing six games with a groin injury and stopped 27 shots for the Coyotes, who have lost six of seven and were shut out for the fifth time. They played their sixth straight game without injured centers Martin Hanzal and Boyd Gordon.

Phoenix defenseman Adrian Aucoin sat out the last two periods after he was struck in the right eye by the puck as Mike Richards flipped it out of the Kings' zone during the final minute of the first. Left wing Raffi Torres, who scored two goals against the Kings in a 4-3 loss at Staples Center on Dec. 26, finished serving a two-game suspension he received from the NHL after taking a run at Minnesota's Nate Prosser from behind last Saturday.

Game notes

The Kings have killed off 28 consecutive power plays, and their opponents are 3 for 76 with the man advantage over the last 21 games. ... The Phoenix-Winnipeg franchise is in its 32nd season and still hasn't won a division title. The Coyotes are fourth in the Pacific and trail first-place San Jose by five points. ... Tippett spent three seasons with the Kings as an assistant under Andy Murray.