Drew Doughty got the Kings on the board first at the 7:49 mark of the first period with a spectacular end-to-end goal.
After a scoreless second period, the Devils knotted it up 1-1 with 2:59 gone by in the third period after Ryan Carter tipped in a shot from the point by Marek Zidlicky.
But it was the Kings who got the last laugh once again, thanks to a terrific effort by Jeff Carter to score the game-winning goal in the first overtime.
After his original pass attempt went astray, Carter regained possession, circled around the net and hammered home the wrist shot from the left slot, giving the Kings a 2-1 victory in Game 2.
Los Angeles is now a perfect 10-0 on the road this postseason, and this might have been the final away game for the Kings.
The series will now shift to Los Angeles for Game 3 and 4.