With Dwight King's go-ahead goal 1.47 minutes into the third period breaking the deadlock, the eighth-seeded Kings took a commanding 3-0 lead in the best-of-seven Western Conference final.
Los Angeles, who crushed the third-seeded Coyotes 4-0 in Phoenix on Tuesday, have now won eight consecutive post-season games but they are taking nothing for granted ahead of Sunday's Game Four, also at home.
"You don't get anything for three wins," Kings goaltender Jonathan Quick told reporters after producing another superb performance with 18 saves. "We're going to go back to work tomorrow to get ready for Game Four.
"Obviously you've got to enjoy the victory for a few minutes here. That's why you work so hard. We know what we have ahead of us. We know (Phoenix) is going to come out hard in Game Four."
Phoenix, who edged Los Angeles in a scoreless first period with 11 shots on goal versus eight, opened the scoring when center Daymond Langkow powered home a wrist shot 1.03 minutes into the second period.
The Kings responded just 2.07 minutes later, Slovenian center Anze Kopitar breaking clear following assists by Dustin Brown and Justin Williams before deftly backhanding the puck past goalie Mike Smith into the net.
With cries of "Let's Go Kings" echoing around the Staples Center, Los Angeles struck early in the third period when left wing King scored with a wrist shot in the top corner of the net, his fifth goal in five games, to put his team 2-1 ahead.
"I got the puck off the wall and had a little more time than I expected," said King. "Once I got close enough to the middle, I had a great chance to shoot and that's what I did."
Roared on by an electrified sellout crowd of 18,367 with many of them waving their Kings towels in the air, the home team held on to push the Coyotes to the brink of elimination.
The Kings upset the top-seeded Vancouver Canucks in the first round of the playoffs before going on to sweep the second-seeded St Louis Blues and advance to the Western Conference final.
"I thought we were playing fine," Phoenix captain Shane Doan said. "I don't think we played bad for very much of the game.
"For the most part, we played the way we wanted and couldn't find a way to score. We had a couple of chances that we couldn't bury and that was the difference."
Asked to assess his team's feelings after trailing 0-3 in the series, Doan replied: "None of us planned on being in it (a 3-0 hole). I don't think it's disbelief but I think it's disappointed."
Coyotes goaltender Smith kept his team in the game by stopping 26 shots in an inspired performance, but he was unable to save King's shot to the glove side in the third period.
"It was a tight game all the way through," Phoenix coach Dave Tippett said.
"We didn't create a lot, but we hung around, gave ourselves a chance to win. The level is being raised here. We just haven't been able to get to the next level."
The Coyotes were without forward Martin Hanzal, who was suspended one game by the league on Wednesday for a harsh hit on Kings captain Dustin Brown in Game Two.