Former Flyer Justin Williams set up the breakaway.
"Their one D-man came down the wall and other D came to me," Williams said. "I wasn't sure if Kopitar was alone or not, so I just threw it over there."
"It feels great," Kopitar said. "I wanted to make sure I went to the middle. I yelled for the puck and I don't know if he heard me or not, but he chipped it perfectly."
The Kings, seeded eighth in the West, are 9-0 in road playoff games this season. They have won their last 11 road playoff games dating back to last year. Both streaks are NHL records.
New Jersey, aiming for its fourth title in the last 17 years, will try to even the series Saturday night in Newark.
Devils coach Peter DeBoer said his team made "a little bit of a bad read" on the game-winning sequence.
"There were a couple of [aggressive] decisions there, but we're playing to win the game. I don't make any apologies for that. We made a mistake and they capitalized."
With the score knotted at 1-1 midway through the third period, New Jersey defenseman Mark Fayne joined the rush and fired wide of an open net in front.
Los Angeles dominated the final 10 minutes of regulation, and Devils goalie Martin Brodeur made brilliant late stops on Drew Doughty, Dustin Penner, and Mike Richards to keep the game tied.
Road teams are 15-9 in OT games in this year's playoffs.
The Kings outshot the Devils, 25-18, and won 55 percent of the faceoffs.
"We're going to have to find another level. I feel we have another level," DeBoer said. "I thought we came out a little tentative, as was expected for a Stanley Cup Final game. We got better as the game went on, but that's a team we have to play 60 minutes against."
Added DeBoer: "The good news is we started in the same hole against Philly and started in the same hole against the Rangers, and we responded to the situation in the right way. I expect the same thing."
New Jersey had few scoring chances in the first two periods, but it got a fortuitous bounce and tied the game 1-1 late in the second.
A left-wing drive by Devils defenseman Anton Volchenkov apparently caromed off Kings defenseman Slava Voynov and past goalie Jonathan Quick with 1:12 left in the second period.
It was Volchenkov's fourth goal in 80 career playoff games - and first in 19 contests in this year's wacky tournament.
There are a lot of star-quality snipers playing in the Finals, including New Jersey's Zach Parise, and Ilya Kovalchuk, and Los Angeles' Kopitar and Jeff Carter.
Yet two unlikely players exchanged goals in the first two periods.
Volchenkov did the honors for the Devils, and it was a former Flyers draft pick named Colin Fraser who jump-started the Kings by scoring the first playoff goal of his career.
A fourth-line center, Fraser took a feed from Jordan Nolan and one-timed a right-circle shot past an unsuspecting Brodeur midway through the first period, giving the Kings a 1-0 lead.
Selected by the Flyers in the third round of the 2003 draft, Fraser managed just two goals in 67 regular-season games.
The Kings have the Flyers' first three picks from the 2003 draft - Carter, Mike Richards, and Fraser. If you thought it would be Fraser who would be the biggest factor in the first period, you must be related to the Amazing Kreskin.
Nolan did the dirty work on Fraser's goal as he won a board battle behind the net before feeding his teammate. In 2004, Fraser was part of a multiplayer trade in which the Flyers acquired Alexei Zhamnov from Chicago.
Breakaways. Brodeur started his 200th playoff game. Only Patrick Roy (247) has more playoff starts.. . . Parise or L.A.'s Dustin Brown will become the second U.S.-born captain to hoist the Cup. Derian Hatcher, a former Flyer, was the first as he captained Dallas past Buffalo in 1999. . . . Commissioner Gary Bettman, in his pregame address, said the players association and NHL have agreed to meet in the coming weeks and begin discussing the new collective bargaining agreement. . . . Nicklas Lidstrom has made a decision about his future. The 42-year-old will announce Thursday whether he's returning to play a 21st season with the Red Wings.
Contact Sam Carchidi at scarchidi@phillynews.com or
on Twitter @BroadStBull.
