With a buzzing home crowd prepared to celebrate the Kings' first trip to the championship series since 1993, Phoenix crashed the party and cut the Western Conference semi-final series deficit to 3-1.
Shane Doan scored a power-play goal in the first period then netted again in the second while Phoenix's defence contained the Los Angeles attack to earn their first win of the series.
Goaltender Mike Smith continued his strong playoff run with a 36-save shutout to give the Coyotes a fighting chance in the series, although the odds are stacked against them as only three NHL teams have come back from 3-0 down to win.
"That's what sports is about, doing things that no one has done in a while when the odds are stacked against you," Doan said.
"I don't think anyone was excited about being down 3-0. We had to be better."
The Kings were looking to make history of their own and will rue their missed opportunities as they seek their first ever championship.
Not since Wayne Gretzky led the franchise to the championship series 19 years ago have the Kings positioned themselves to play for the title.
But even with members of the Kings' 1993 team in attendance and a frenzied crowd waving white towels, Phoenix held firm.
Los Angeles outshot the Coyotes 36-21 but could not find a way past Smith, who made a series of reflex saves.
Trevor Lewis had a breakaway look at a goal in the first but was stopped by Smith. In the second, with Smith scrambling to get back in front of the net, the Kings' Anze Kopitar sent a pass from behind the goal to a free Dustin Brown but Phoenix converged to deny the prime scoring chance.
The third period was more of the same for the Kings, who pulled goaltender Jonathan Quick for an extra attacker in the final minutes but could produce no magic. Quick finished with 19 saves.
"I think you have to give them credit right now," Brown said. "They came in down 3-0 on the road and played their game to a tee. Tonight we couldn't find a way to score a goal."
It was a rare struggle for a Los Angeles team that has managed to turn a mediocre regular season into a red-hot playoff run.
Entering the post-season as an eighth seed, the Kings beat the top seeded Vancouver Canucks in the first round of the playoffs then the second seeded St Louis Blues in the second then won the first three against the Coyotes.
Game Five will be played in Arizona on Tuesday.
"We're still in a good position," Kopitar said. "We have to step up, refocus and make sure we have a lot of energy."