Fourth-line centre Colin Fraser scored in the first period for the Kings and smooth-skating Slovenia star Anze Kopitar finished it off 8:13 into overtime for a 2-1 win Wednesday over the New Jersey Devils.
Anton Volchenkov replied in the second for the disappointing Devils.
In a tight game without much offence from either side, New Jersey's attack disappeared for long stretches before a soldout crowd of 17,625.
"We'll be better on Saturday night," said a grim-faced Devils coach Peter DeBoer.
"I don't believe we deserved to win tonight, that's the bottom line and that's what happened. If we had have won, we would have been sneaking one out."
Justin Williams found Kopitar with a backhand pass from his own blue-line as the Devils seemed to run into each other. The Kings star raced in alone, deking Martin Brodeur before slipping it over him with a forehand for his seventh of the playoffs.
"We made a mistake. They capitalized," DeBoer said.
Los Angeles, the eighth seed in the West, is now 9-0 on the road in the playoffs. For goalie Jonathan Quick, it was a record 11th consecutive road playoff win dating back to last year, erasing Billy Smith's mark for the 1979-80 New York Islanders.
Kings coach Darryl Sutter downplayed the road warrior angle.
"We've won one on the road now," he said, focusing exclusively on the final. "The season started tonight."
Quick and Kopitar, however, pointed to the Kings' work ethic for their success away from home.
Whatever the reason, a home loss is exactly what the Devils wanted to avoid. Especially against a team feeling confident on the road.
Teams winning Game 1 of the final have gone on to win the Cup in 55 of 72 seasons (76 per cent) since the league went to the best-of-seven format in 1939.
Boston bucked that trend last season, however.
This promises to be a series where scoring chances won't come cheaply or in bunches.
The Devils had five shots in the first period and just four in the second, but still managed to pull even at 1-1 late in the second period on a deflection off a Kings defenceman.
Los Angeles outshot New Jersey 22-16 in regulation and had a 3-2 edge in OT
"(There) wasn't much going on offensively for either team," Sutter said. "The way the teams play, it's such tight quarters out there ... Pretty evenly matched teams. There's probably going to be more than one overtime game."
For all the talk of Quick as the Kings uber-stopper in goal, New Jersey made it easy for him for long stretches. He was there when needed, however.
Brodeur, in his 200th playoff game, was also sharp in a third period that eventually opened up.
It marked the 24th overtime game of the 2012 playoffs. And the first Game 1 of the final to go to overtime since 2002, when the visiting Carolina Hurricanes defeated the Detroit Red Wings 3-2.
The Kings are 3-0 in overtime in these playoffs. The Devils are 4-2.
The game opened to a sea of red-clad fans waving white towels in the Prudential Center stands.
But it proved to be a less colourful start on the ice, with both teams looking to nip the other's offence in the bud.
The first shot of the game took more than three minutes for the Kings to record, after a poor defensive pass behind the Devils' net led to a giveaway.
"We came out a little slower than we wanted to," said Kopitar, who credited the line of Fraser, Brad Richardson and Jordan Nolan for sparking the team.
It was more than six minutes into the game before New Jersey finally tested Quick.
"We're going to have to find another level," DeBoer said. "I feel we have another level.
"I thought we came out a little tentative, as was expected for a Stanley Cup final game. I thought we got better as the game went on. But that's a team you've got to play 60 minutes against.
"The good news is we started in the same hole against Philly, we started in the same hole against the Rangers and we responded to this situation in the right way the last two rounds and I expect the same."
The few early Los Angeles chances, meanwhile, came from New Jersey errors in the defensive zone.
That led to the first goal as Nolan outmuscled a Devils defenceman behind the goal and sent the puck to Fraser, who snapped a low shot past Brodeur at 9:56 for his first of the playoffs.
The Kings fourth-line centre had just two goals in the regular season.
When New Jersey threatened in the first, Quick was there. He made two good stops during the lone power play of the period.
The Devils came out hitting early in the second, bringing the crowd back into the game. But its offence — and power play — remained dormant.
New Jersey did not put a shot on goal for the first 14:30 of the second period and even that one seemed slightly dubious — a timid redirect during a penalty kill.
Quick eventually had to make a save, using his glove to stop Dainius Zubrus.
New Jersey finally beat Quick when Volchenkov's shot from the point bounced in off Kings defenceman Slava Voynov at 18:48 of the period.
The Devils pressed to open the third. A New Jersey goal at 3:58 was correctly disallowed as Zach Parise's hand swept the puck in during a goalmouth melee. Video review confirmed the officials' call.
Nolan showed his disregard for Brodeur midway through the third, slapping his stick repeatedly at the future Hall of Famer in search of a loose puck.
At the other end, Devils defenceman Mark Fayne missed an open net, shooting wide as the puck came across the crease.
Brodeur then made three saves, one after another, on one Kings shift.
The Devils and Kings are meeting in the Stanley Cup playoffs for the first time.
The Kings are one win shy of the NHL record for road victories in a post-season (10) shared by a group of clubs that includes the New Jersey Devils in their Cup-winning 1995 and 2000 playoff runs.
They are also the first team to record 11 straight away wins over multiple playoff years.
For the Devils, seeded sixth in the East, Wednesday marked the first time they had opened a series at home this post-season.
It was just the third time the two teams have met this season. New Jersey won both regular-season encounters in October.Suggest a correction