The Kings took a 3-0 lead in the series but lost the next two matches as the Devils belatedly found their form.
But there was no stopping them in game six, with Jeff Carter and Trevor Lewis each scoring two goals.
Team captain Dustin Brown scored the opening goal 11 minutes into the first period and Matt Greene rounded out the scoring in the final stanza.
Goaltender Jonathan Quick made 17 saves in another fine showing.
Adam Henrique scored New Jersey's only goal in the second period, by which point the Kings had already opened up a 4-0 lead.