The Kings lead the Western Conference finals 3-0.
"We wanted to have our own push in front of our owns fans, show our push," said Kings forward Jarret Stoll, whose hustle set up King's goal. "It took us a while to get our own game (going), but we did, especially in the third period."
Anze Kopitar also scored to help the eighth-seeded Kings improve to 11-1 in their improbable post-season run. Despite trailing in a game for the first time since April 28, King scored his fourth goal in three games against the Coyotes, who face a deficit only three teams have overcome in NHL playoff history.
Game 4 is Sunday at Staples Center.
Mike Smith stopped 26 shots in a standout performance for the third-seeded Coyotes, who must win four straight to reach their first Stanley Cup final in club history.
Although the Kings have won eight consecutive playoff games during this rampage through the West bracket, they fell behind for the first time in nearly 18 periods when Daymond Langkow scored on a breakaway for Phoenix early in the second period. That deficit disappeared just over 2 minutes later on Kopitar's breakaway goal.
King came through again 1:47 into the third, beating Smith high to the glove side. The massive rookie scored two goals in the series opener and added the winner in Game 2.
In front of a long-suffering crowd gratefully enjoying its unexpected good fortune after decades of disappointment, the Kings dominated the third period in front of Quick. They forechecked relentlessly in the final minutes, forcing Smith to play a long stretch without his goal stick because Phoenix couldn't clear the zone so he could retrieve it.
Los Angeles largely dominated the first two games of the series in Glendale, outshooting the Coyotes 88-51 while winning by a combined 8-2. Phoenix had no more luck than Vancouver or St. Louis against the surprising No. 8 seeds, who finished two points behind the Pacific Division champion Coyotes in the regular season before steamrolling the West's top two teams in a combined nine games.
Phoenix played Game 3 without forward Martin Hanzal, who served a one-game suspension for boarding Dustin Brown in Game 3. Coyotes captain Shane Doan, who escaped suspension for his own hit, took up the job of agitating Brown, facewashing the Kings' high-scoring captain with his glove during one scrum.
After Smith came up with several stellar saves during a scoreless first period, Keith Yandle slipped a long pass behind Mike Richards to Langkow, who beat Quick between the legs for his first goal of the post-season 1:03 into the second. Los Angeles hadn't trailed since the first period of Game 1 in its second-round series with St. Louis 19 days ago.
Staples Center briefly fell silent, but reached full roar moments later when Brown found Kopitar with a long pass behind the Phoenix defence. The Slovenian star beat Smith with a backhand for his fifth goal of the playoffs.
The teams were even in goals and shots heading to the third period, but King quickly put Los Angeles ahead with the latest impressive play of his incredible first NHL playoff run. Moments after Smith made a spectacular point-blank save on Stoll, King collected the puck during a delayed penalty and wired a high shot past Smith's glove into the top corner of the net.
Phoenix responded to its deficit with more physical play in Game 3, although keeping most of it within legal limits after the borderline goonery of the Game 2 blowout. The Coyotes inserted enforcer Paul Bissonnette into their lineup for the first time since Game 4 of the opening round.
NOTES: The game was the first of six playoff contests in four days at Staples Center, where the NBA's Lakers and Clippers will host back-to-back second-round playoff games this weekend. The Tour of California — the nation's largest cycling race — also finishes outside the arena about 30 minutes before the puck drops on Game 4 Sunday. ...Marc-Antoine Pouliot took Hanzal's spot in the Coyotes' lineup, but Langkow moved up to Hanzal's place on a line with Taylor Pyatt and Radim Vrbata. Bissonnette replaced Gilbert Brule. D Adrian Aucoin has missed the entire series with an injury. ... The Kings have won seven straight road games, and they stuck with coach Darryl Sutter's scheme to keep the road vibe at home by staying in a hotel across the street from Staples Center on Wednesday night. ... USC QB Matt Barkley attended the game.