The Kings, who have done their business the hard way in their lay-off run with three Game Seven wins on the road and battled back after falling behind by two goals in each of their two wins at home changed the script in their visit to Broadway.
Los Angeles put themselves firmly in the driver's seat with pinpoint shooting and a spectacular performance by goaltender Jonathan Quick.
The winners converted three of their modest 15 shots on goal, while Quick saved all 32 shots from the Rangers, who failed to take advantage of six power play chances.
"He was obviously the best player on the ice," said Rangers coach Alain Vigneault.
Kings coach Darryl Sutter said the power play was the key.
"They didn't score on any of them," Sutter said.
"I think the second period was probably the most important part of it. We scored on the power play and they didn't. That's a big difference."
Now it is the Rangers who must be comeback kings if they are to win their second Cup in 20 years and third since 1940.
Only one team has ever overcome a 3-0 deficit to win the final - the Toronto Maple Leafs, who notched four successive wins to beat the Detroit Red Wings in 1942.
"We're happy we're up 3-0," said right-winger Justin Williams, who vowed the Kings would not suffer from overconfidence since they stormed back from a 3-0 deficit in the first round to beat San Jose.
"But we know as good as anybody that 3-0 is not four. Just because you're leading the series doesn't mean you've won anything."
A last-second goal at the end of the first period by Jeff Carter gave the Kings a 1-0 lead, and the Western Conference champions increased their advantage with second-period goals by defenseman Jake Muzzin and Mike Richards.
Quick was sensational at the net, stopping all 32 of New York's shots on goal for the Kings, who can clinch their second Cup in three years with a victory at the Garden in Game Four on Wednesday.
The fast-paced first period was marked by swarming defense on both sides and only nine shots on goal.
New Yorks left winger Mats Zuccarello had New York's best chance, when he swept in with just under five minutes to go in the period to put his stick on a rebound in the crease just to the right of Quick.
Zuccarello tried to stuff it in, but Quick lunged along the ice and managed to get his stick on the puck to turn it away at the last instant.
The period looked set to end scoreless until one last Los Angeles rush as the clock ticked down.
Williams centred the puck across to Carter who rifled a wrist shot past New York's Swedish goalie Henrik Lundqvist for a goal that grazed off defenseman Dan Girardi's skate.
The Kings increased their lead to 2-0 less than five minutes into the second period when Muzzin snapped a long-range shot from the blue line past Lundqvist, who was screened by Carter camping out in front of the net on a power play.
The Rangers had the man advantage three times in the second period and on two of them mounted furious attacks that totalled seven shots on goal but stifled each time by acrobatic saves from Quick.
With 2:46 left in the period, Mike Richards cashed in a 2-on-1 break by snapping home a return pass from Kyle Clifford past Lundqvist to end the scoring.
The third period was played in virtual silence at the famed midtown Manhattan arena after thunderous roars had encouraged the Blueshirts from the opening faceoff until the Kings had put their stamp on the game.
"Nothing's done, nothing's finished," cautioned Quick, who grew up in nearby Hamden, Connecticut as a Rangers fan.
"We know that winning the fourth game is always the hardest."
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