Brian Gionta and Travis Zajac scored during New Jersey's first two power plays, but it wasn't enough as the Devils ended a five-game road trip with their fourth straight defeat - matching their longest losing streak of last season. Martin Brodeur made 26 saves.
The Kings, coming off a 3-1 victory over Calgary on Saturday, have won consecutive games for the first time since beating St. Louis and the New York Islanders last month.
Mathieu Garon made it possible for the Kings to get to overtime, kicking out a last-second shot from the high slot by Brian Rafalski for his 20th save after Scott Gomez passed the puck from behind the net.
Brodeur made an even better save 25 seconds into the extra session, sprawling to his right to thwart Dustin Brown after a perfect centring pass through the crease from Kopitar.