Stoll's tally midway through the second period restored the Kings' two-goal cushion and Quick stood up to a furious Devils onslaught in the final frame, turning aside all 20 shots he faced.
Justin Williams and Michal Handzus also scored for Los Angeles, which posted its first 5-0 start at home since Wayne Gretzky's first season with the team in 1988-89.
New Jersey, meanwhile, dropped its fourth in five games.
Matt Taormina got the Devils' only goal and Martin Brodeur stopped 20-of-23 shots in the loss.
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