Eighth-seeded Los Angeles improved to 15-2 in the postseason and jumped to a 3-0 lead in its fourth straight series - a first in NHL history.
Game 4 is Wednesday night at Los Angeles.
"We're almost where we're trying to go, but we haven't won anything yet," captain Dustin Brown said. "We know what we have a chance to do, though. Having an opportunity to win a championship here could get rid of a lot of frustration for a lot of people."
Simon Gagne returned to the Kings' lineup, completing a remarkable comeback from a concussion. The former Flyer hadn't played since Dec. 26, when the veteran left wing's career was threatened by his latest head injury. He got a large ovation from the sellout crowd at Staples Center when he was announced in the lineup.
Gagne is in his first season with the Kings, who signed the seven-time 20-goal scorer as a free agent.
He had three shots on goal and played 6 minutes, 39 seconds.
Martin Brodeur stopped 17 shots, but the Devils couldn't beat the spectacular Quick or his penalty-killers, who turned aside six power plays. New Jersey must accomplish just the fourth comeback from an 0-3 series deficit in NHL playoff history to win its third title.
New Jersey has been pretty good in the finals, but nothing has been able to slow down these Kings, who seem destined to become the first No. 8 seed to win the Stanley Cup.
The Devils had never lost three straight Stanley Cup finals games in the franchise's five appearances. New Jersey hadn't lost three straight games this season since late February.
Although the Kings have been improbably dominant during the postseason, the Devils gave Los Angeles plenty of trouble in the Kings' two overtime victories in Newark last week. New Jersey's strong forechecking and Brodeur's solid goaltending nearly overwhelmed the Kings, who had to rely on Quick and their own stellar penalty-killing to reach overtime.
The Kings needed their penalty-killing again in the first period of Game 3 after Carter took a 4-minute penalty for high-sticking Adam Henrique while Los Angeles already was short-handed. Los Angeles killed one minute of 5-on-3 play before Marek Zidlicky lopped two more minutes off the power play with a penalty of his own to prevent a breakaway. New Jersey had just one shot to show for all that advantage during the scoreless first period.
The Devils again dominated the puck early in the second period, keeping it in Los Angeles' end for long stretches, but Quick made saves with everything from his blocker to his shoulder to keep the puck out.
But the Kings went ahead when Dwight King created a scoring chance with a big hit, eventually hacking at the puck underneath Brodeur's pad in front. Martinez joined the effort with Trevor Lewis and got credit for the goal when the puck finally trickled in, scoring his first goal in his 23rd career playoff games. The Devils complained play should have been stopped.
Late in the period, Kopitar extended the lead on a stellar rush by the Kings' top line. Justin Williams moved the puck into the zone and found Brown, who feathered a cross-ice pass to Kopitar for the Slovenian star's eighth goal of the postseason, giving Los Angeles its first two-goal lead since Game 2 of the Western Conference finals.
The Kings finally got a power play early in the third period, and Carter found Brodeur's top shelf with a pass from Richards. Williams then caught the Devils' penalty-killers napping, and the celebration was on.
Staples Center was packed to the rafters well before Wayne Gretzky took the ice for the ceremonial opening faceoff.
Los Angeles' long-suffering hockey fans hadn't seen a Stanley Cup finals game since 1993. The roaring crowd gave a standing ovation to Gretzky, the driving force behind the Kings' only other finals appearance.
The Pittsburgh Penguins acquired goaltender Tomas Vokoun from the Washington Capitals for a seventh-round draft pick.
Vokoun spent only one season with the Capitals and is set to become an unrestricted free agent on July 1.