Los Angeles has lost four of its past five games (1-4-0) and seven of its past nine home games (2-7-0).
"It gets harder with each and every loss, really," Kings center Anze Kopitar said. "You dig a bigger hole every night and it's hard to get out of it. Like I said, when things don't go right everything's going wrong against you. But then again, it's up to us to come up out of that hole."
Palmieri put the Devils back in front 3-2 at 10:57 of the second period after Kempe made it 2-2 at 6:59. It was Palmieri's fourth multigoal game after scoring two goals in each of the first three games of the season.
Butcher made it 4-2 at 12:28 when Kings defenseman Dion Phaneuf accidentally deflected a long shot into his own net.
"It's a fresh start," Palmieri said of the three-game California trip. "You can't worry about our road record this year (3-10-1), and you can't worry about what happened in October and November. It's about what we're doing now and it's something to build off of, for sure."
Jake Muzzin had a sharp-angle shot hit the post and crossbar at 13:31. It was ruled a goal by the on-ice officials, but the call was overturned when video review showed the puck never crossed the line.
Clifford pulled the Kings within 4-3 at 17:37.
Hischier extended the lead to 5-3 at 11:06 of the third period, and Blake Coleman scored into an empty net at 19:52 for the 6-3 final.
New Jersey took a 2-1 lead 25 seconds into the second period on Zajac's ninth goal.
Palmieri put the Devils up 1-0 on the power play at 13:49 of the first period before Leipsic tied it 1-1 at 15:41.
It was the third power-play goal for New Jersey in its past 15 games, having gone 2-for-35 prior to scoring on its first opportunity.
