The brilliant Jonathan Quick recorded his third shutout of the post-season while Anze Kopitar, Alec Martinez, Jeff Carter and Justin Williams all scored to hand the Kings a commanding 3-0 lead in the best-of-seven series.
The Kings can now finish off the Devils and hoist the Stanley Cup on home ice if they can complete the unlikely sweep with a Game Four win at the Staples Center on Wednesday.
The victory was another step in a remarkable journey for the Kings, who scraped into the post-season as the eighth seeds after losing more games than they won but have reigned supreme in the play-offs, boasting a 15-2 record.
Only one team, the 1942 Toronto Maple Leafs, have clawed back from 3-0 deficit to steal the Cup but the cautious Kings are not planning a victory parade just yet.
"We're going to keep pushing forward," Los Angeles' Justin Williams said. "We're a focused group right now, we're not going to let anything get in our way.
"We certainly don't want to get back on that plane.
"We're tasting that we're close and that should drive us even more."
Boasting a perfect 10-0 on the road this post-season, the Kings showed they could be just as dominant at home, with Quick stopping all 22 shots he faced to demonstrate why he is the leading candidate for the Conn Smythe trophy as the Stanley Cup's most outstanding player.
Quick has received plenty of support with defensemen throwing themselves in front of shots, while the rest have been swallowed up by the Kings netminder, who has surrendered just two goals in three games on more than 70 shots.
"You need outstanding goaltending to win play-off games," said Kings coach Darryl Sutter. "He's (Quick) given us that."
With the Staples Center's other tenants, the NBA Lakers and Clippers, out of the play-offs the Kings have had the sporting spotlight in Los Angeles to themselves.
The game was the first Stanley Cup contest played in Los Angeles since Wayne Gretzky led the Kings to the finals 19 years ago and a record crowd of 18,764, including A-list celebrities like former England captain David Beckham, arrived at the Staples Center ready to party.
Gretzky, nicknamed "the Great One" and whose bronze statue stands out front of the arena, had maintained a low profile during the Kings post-season charge but was front and centre for Game Three as he performed the ceremonial puck drop to a standing ovation from the adoring crowd.
Following a scoreless opening period, the Devils had the early run of play in the second but again it was the Kings who were on the scoreboard first when Martinez jammed home a loose puck from a goal-mouth scramble after Martin Brodeur had denied Dwight King twice from close range.
The Kings added to their lead with 4:53 left to play in the second when Kopitar, who scored the overtime winner in Game One, took a pinpoint feed from captain Dustin Brown and re-directed it past a helpless Brodeur.
After a pair of 2-1 overtime nail-biters in New Jersey, the Kings ended the drama early with powerplay tallies at the start of the third period from Jeff Carter and Justin Williams, sparking chants of "We want the Cup!" from ecstatic home fans.
In an extraordinary post-season that has seen the Kings set a string of records and firsts perhaps the most impressive is that they have charged to 3-0 leads in all four series.
The Devils had their chances and enjoyed a four-minute man-advantage late in the opening period when Carter was sent off for high-sticking, but could not convert any of their five powerplays, including a five-on-three. Los Angeles are a perfect 12-for-12 on the penalty kill for the finals.
"We created some real good chances early, he (Quick) made some saves," said Devils coach Peter DeBoer. "The frustrating part is you're creating some quality chances, you're getting some quality shots and they're not going in.
"I don't care what the scoreboard said. We battled right to the buzzer and we'll do the same on Wednesday night."