Los Angeles' more-heralded ex-Flyers, Richards and Carter, were nonfactors and were each minus-1.
Kopitar scored on a dazzling move against goalie Martin Brodeur, who played superbly. Williams made the breakaway possible.
"Their one D-man came down the wall and the other D came to me," Williams said, referring to the defensemen. "I wasn't sure if Kopitar was alone or not, so I just threw it over there. It's just an area pass where you hope the guy skates into it."
"I wanted to make sure I went through the middle," Kopitar said. "I don't know if he heard me or not. I yelled for the puck. He chipped it obviously perfect, right on my tape."
Stunningly, 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 from last year. Both streaks are NHL records.
"I think we've outworked teams," said Kings goalie Jonathan Quick, the Conn Smythe Trophy favorite as the MVP in the playoffs. "I think whoever wins this series is going to be the team that outworks the other."
If Game 1 was an indicator, this will be a tight-checking series that will not feature a lot of scoring chances. The Kings outshot the Devils, 25-17, and New Jersey had just five shots in the first half of regulation.
"Both are very good defensive teams first," Kings coach Darryl Sutter said.
The Devils, aiming for their fourth Cup in 17 years, "don't give up a whole lot," Kopitar said. "You have to be careful going through the neutral zone that you don't make any turnovers, because they've got some speedy forwards who obviously can finish. You have to await turnovers and just make sure you make strong plays."
Both teams said they were off their games in the opener. The Devils' forecheck, so dominating in their playoff wins against the Flyers and New York Rangers, was noticeably ineffective and will have to improve if they are to tie the series.
"We didn't execute well enough in our dumps, on our routes," said Devils forward Travis Zajac, who was minus-2 in the opener. "We didn't win enough battles to keep pucks alive, keep the forecheck going."
Devils coach Peter DeBoer said the Devils "have to find another level. I feel we have another level. 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, whose team was seeded sixth in the East: "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."
Contact Sam Carchidi at firstname.lastname@example.org. Follow on Twitter @BroadStBull.