Palmieri scored twice in a matchup of conference cellar dwellers as the Devils snapped a six-game losing streak and got just their third victory away from home.
"This is a big road trip for us. We wanted to get off to a good start," said Palmieri, who leads the Devils with 14 goals. "We scored timely goals and that's what you need to do. It's a fresh start. You can't worry about what happened in October and November."
The right wing had seven goals in New Jersey's first four games -- all wins -- but had been in a slump since then. Coming into Thursday, he had just one goal in his past nine games. He also had not fared well against the Kings, going without a goal in his last 13 games against Los Angeles and scoring only two in 18 meetings.
Both his goals came on wrist shots that beat Jonathan Quick to his glove side.
Palmieri opened the scoring on a power-play goal with six minutes remaining in the first period off a pass from Taylor Hall, who had three assists. Palmieri then put the Devils up for good, 3-2, midway through the second period on a snap shot.
New Jersey was clinging to a 4-3 lead midway through the third when Nico Hischier provided an insurance goal. He got position in the slot and was able to redirect Sami Vatanen's shot past Quick for his sixth of the season.
Blake Coleman added a late empty-net goal for his ninth.
Travis Zajac and Will Butcher each had a goal and an assist. Keith Kinkaid, pulled after allowing four goals in two periods during Monday night's loss to Tampa Bay, bounced back with 29 saves.
"I thought his puck play was strong and his decisions were good," Devils coach John Hynes said. "He did a good job of seeing pucks through traffic. He came up big for us in certain situations."
Brendan Leipsic, Adrian Kempe and Kyle Clifford scored for the Kings, who have dropped four of five and are last in the NHL with 21 points. Quick stopped 29 shots.
Leipsic scored his first goal with Los Angeles and third of the season on a wrist shot from just inside the right circle that went through Kinkaid's legs with four minutes remaining in the first to tie it at 1. The left wing was claimed off waivers from Vancouver on Monday and was playing in his second game for the Kings.
Kempe's goal in the second came on a pass from Drew Doughty. The assist by Doughty gave him 334 for his career and made him the franchise leader among defensemen, surpassing Rob Blake.
"We're obviously super frustrated. It's another game that we didn't perform well enough. It's frustrating. It's embarrassing. It's a lot of things," Doughty said.
RW Nikita Scherbak's debut with the Kings was pushed back another game due to visa delays. The 23-year-old Russian, claimed off waivers Sunday from Montreal, could be on the ice for Los Angeles' next game Saturday. ... Zajak's goal was only the ninth time since 2000-01 that the Devils have scored in the first 25 seconds of the second period. ... Kempe has two goals in his past three games.
Devils: Continue their three-game road trip Sunday at Anaheim.
Kings: Host the Vegas Golden Knights on Saturday.
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Palmieri lights lamp twice in Devils' win
Kyle Palmieri scores the game's first goal on a power play, then beats Jonathan Quick to break the 2-2 tie and help the Devils to a 6-3 win.