Kopitar scored an empty-net goal with 2.9 seconds left. Schneider made 19 saves.
Friday's game was the Kings' first visit to the Prudential Center since playing the Devils in the 2012 Stanley Cup finals.
The Kings nearly scored 7:33 into the third period. Muzzin centred a puck from the left side of the blue line. New Jersey defenceman Andy Greene put out his stick and deflected it on goal, where Schneider alertly made the save.
But King was penalized for hooking 50 seconds into the power play and sat for two minutes.
Harrold was the recipient of a hit to the head by Jordan Nolan with 1:31 left in the second.
The centre put his shoulder down and levelled Harrold with a shot to the side of his head. Harrold was face-down on the ice, but, after play was stopped, he managed to skate off on his own. Harrold returned to regular shifts in the third period.
The Devils were the aggressors in the scoreless first period, gaining a 12-6 advantage in shots.
NOTES: Jaromir Jagr has 120 career game-winning goals, just one behind the NHL record held by Gordie Howe. ... Patrik Elias returned after a six-game absence for the Devils, who also got back Stephen Gionta.