Having taken a 3-0 lead in the title-deciding series, Los Angeles' apparently inevitable charge to glory was halted on Wednesday when the Devils scored their first win.
They followed that with a second on Saturday - a first away defeat for the Kings in this post-season.
Zach Parise put the Devils in front in the first period before Justin Williams levelled things early in the second.
That set the stage for Bryce Salvador to win it for the hosts with a deflected effort later six minutes later.
The third period was a stalemate, with the Devils' goaltender Martin Brodeur finishing with 25 saves.