WATCH: All Kings vs. Devils highlights
"It's nice to get back on board the winning side for a change," Pearson said. "We'd been struggling here a bit so this one's big. Hopefully we can carry it into out next game."
Kyle Quincey scored and Cory Schneider allowed three goals on 12 shots in the first period for the Devils (20-20-9). Keith Kinkaid replaced Schneider to begin the second period and made 13 saves.
Schneider returned to the lineup after serving as backup for two straight games because of an illness.
"It wasn't so much about Cory as it was the team," Devils coach John Hynes said. "We gave up three quick goals and [Kinkaid] has played well so we switched it up. I thought Keith came in and did a good job."
Quincey's shot from the point deflected off the leg of Pearson in the slot to end Budaj's shutout bid 7:19 into the third period.
The Kings, who lost 3-2 at the New York Rangers on Monday despite taking 38 shots, took a 2-0 lead on four shots in the opening 1:46 of the first period against the Devils.
Kopitar scored a power-play goal 50 seconds into the game for a 1-0 lead.
"I think I've been lacking in the shooting part of my game and I want to be a little bit more aggressive," Kopitar said. "Part of that is attacking off the half wall. I had some room and tried to get it on net and fortunate for me, it went in."
Los Angeles coach Darryl Sutter has appreciated the effort Kopitar has put forth this season.
"He's one of the best players in the League," Sutter said. "He's on that level with [Jonathan] Toews and [Patrice] Bergeron, guys like that. He's an awesome player. Other than the goal scoring, I've had no problem with him."