GLENDALE, Ariz. -- It's hard to imagine Dustin Brown's popularity in Arizona falling any lower. The Los Angeles Kings captain is already the most reviled hockey player in the Valley due to a colorful history with the Arizona Coyotes.

Brown somehow added to the venom when he scored a pair of goals in the Kings' 6-2 win over the Coyotes on Tuesday at Gila River Arena. Neither goal was impressive -- one came from the red line; the other from a terrible angle -- but both helped L.A. erase a second-period deficit to post its first regulation win over the Coyotes this season in the series finale between the teams. The goals also mean that Brown has scored five of his seven goals this season against Arizona.

"It's probably just coincidence," Brown said with a smirk. "More importantly, we needed two points against a division rival and we played a solid game -- everyone."

Goaltender Jonathan Quick made 23 saves for Los Angeles, which also got goals from defensemen Alec Martinez, Jake Muzzin, right winger Marian Gaborik and center Vincent Lecavalier. Left winger Jordan Martinook and right winger Anthony Duclair scored for Arizona, which got 20 saves from goalie Louis Domingue before he was pulled early in the third period.

Arizona still won the season series, 3-1-1, but the Kings responded to a lackluster 1-3 performance before the All-Star break with a strong effort in their first game back.

"Everybody in our division is in the same boat," said Kings coach Darryl Sutter, whose team opened up a nine-point lead over San Jose for first place in the Pacific Division. "You're fighting for playoff spots so division games are four-point games.

Coyotes left winger Jordan Martinook gave his team an early lead when he caught Quick napping at 6:13 of the first period. Martinook collected a loose puck and sent a shot from the far boards that Quick misjudged.

Los Angeles tied the game early in the second period with Coyotes defenseman Connor Murphy off for roughing. Muzzin carried the puck down the left circle and beat Domingue high through a screen by Kings center Jeff Carter.

Arizona answered quickly when left winger Max Domi corralled a loose puck to the right of Quick and fed right winger Anthony Duclair in the slot. Duclair spun 180 degrees and beat Quick with a high shot to the glove side at 6:40.

The goal gave Duclair 14 on 64 shots for a shooting percentage of 21.9, which is tops in the NHL for players with 50 or more shots. The goal also seemed to give the Coyotes momentum, but Los Angeles tied the game again on another power play at 9:57 of the second period when Martinez beat Domingue through another Carter screen.

"We're talking about a tight, disciplined stretch drive to try to make the playoffs," Coyotes coach Dave Tippett said. "There's a lot of penalties there that can't be had."

Gaborik gave Los Angeles a 3-2 lead at 18:47 of the second period when Coyotes defenseman Kevin Connauton broke his stick while attempting a shot at the far blue line. The resulting turnover gave the Kings a 2-on-1 and Gaborik held the puck to beat Domingue high to the glove side.

Los Angeles broke the Coyotes' backs only 12 seconds later when Brown's shot from the neutral zone fooled Domingue and skipped into the net with 1:01 left in the period.

Domingue, who was named NHL rookie of the month for January, allowed five goals on 25 shots for the second straight game.

"I felt like my glove hand was pretty awful tonight," Domingue said. "I've got to have a better focus going into those games."

NOTES: Arizona's Dave Tippett coached his 1,000th NHL game on Tuesday. ... Coyotes GM Don Maloney said Monday that he would be surprised if G Mike Smith plays any games in February as he rehabs from abdominal surgery in mid-December that was expected to sideline him eight to 10 weeks. Smith has been out seven weeks. He has resumed skating but likely won't practice with the team for at least two more weeks. ... Coyotes assistant GM Darcy Regier is leaving the organization for unspecified reasons, two NHL sources told ArizonaSports.com. ... Kings LW Milan Lucic returned to Arizona 10 days after he was suspended one game for sucker punching Coyotes defenseman Kevin Connauton on Jan. 23 at Gila River Arena. ... The Kings reached the 30-win mark in their 48th game this season, the fastest they have ever reached that mark.