The Kings, seeded eighth in the Western Conference, improved their playoff record this year to 13-2 and will try to take command of the NHL's championship series when New Jersey hosts Game 2 Saturday.
It was the game's first goal since New Jersey had tied it with a fluke goal 72 seconds before the second intermission. Anton Volchenkov was credited with the goal, although it bounced off the body of a Los Angeles player in front of the net and trickled past Jonathan Quick.
The first Los Angeles goal came midway through the first period when the Kings converted a turnover by the Devils into a one-timer by Colin Fraser that he blasted from the right circle.
New Jersey put the puck in the net early in the third period, but the goal was disallowed when replays showed New Jersey captain Zach Parise had used his glove to shove it over the goal line.
Quick, who has been in goal for all of his team's post-season games this season, made 17 saves. Brodeur stopped 23 shots.