Jarret Stoll and Anze Kopitar also scored to help the Kings win for the sixth time in their last seven games, all with Quick in goal.
Los Angeles improved to 3-1 on its five-game trip in a bid to make the playoffs for the first time since 2001-02.
"We're a young group of guys and it's been a learning experience at times this year," O'Sullivan said. "Since Christmas, we have really picked up our game. We have to keep trying to push forward and make the playoffs. That's our goal."
In the process, the Kings cooled off the Devils who came into the game on a 9-1 run. Dainius Zubrus snapped Quick's shutout bid at 10:41 of the third, on a shot that deflected off a defender. He came close to his second road shutout in a week, having blanked Ottawa 1-0 on Tuesday.
"He's grown very quickly in his time here," Kings coach Terry Murray said. "It's a great opportunity for him and he's taking advantage. He's going to be better because of this group of games we're playing on this roadtrip."
The Kings broke the game open with three goals in the second, capped by O'Sullivan's penalty shot at 14:37. O'Sullivan was awarded the shot when Devils defenseman Mike Mottau gloved a loose puck in the New Jersey crease.
Earlier, Stoll opened the scoring with a power-play goal from the point at 10:23 as Dustin Brown provided an effective screen in front of goalie Scott Clemmensen.
Kopitar made it 2-0 at 12:28, tipping O'Sullivan's shot past Clemmensen.
The Devils thought they got a power-play goal from Zubrus at 3:07 of the first. The score was wiped out by a video review that determined Zubrus kicked the puck into the net as he was knocked to the ice in a goalmouth scramble.
"We got an early goal that they called back," Devils forward Brendan Shanahan said. "It was just going to be one of those nights when things weren't going to come easy for us. We were up against a young team that was working hard, and we didn't respond well to that."
It was the second straight home defeat for the Devils, 5-2 losers to Washington here on Tuesday.
"I wasn't pleased at all with the way we've played at home," Devils coach Brent Sutter said. "We don't find that on the road. We'll have to correct it."
Notes: The game kicked off a five-game homestand for the Devils. They played nine of their previous 12 on the road. ... Clemmensen faced the Kings for the first time. ... Devils D Colin White missed the game after injuring a hand Friday night in the Devils' 5-1 win in Atlanta. Jay Pandolfo was the other New Jersey scratch. ... The Kings scratches were John Zeiler, Denis Gauthier (third of a five-game suspension for a hit on Montreal's Josh Gorges on Jan. 31) and Tom Preissing (undisclosed illness).... Raitis Ivanans of the Kings scored a quick knockdown decision over Mike Rupp in their first-period fight. ... The Kings conclude the road trip Tuesday night on Long Island.
