The Kings swept a home-and-home series with the Ducks, having captured a 2-1 shootout decision in Los Angeles Wednesday.
It was the third straight win for Los Angeles and the third consecutive loss for Anaheim.
Kopitar tipped in a shot to snap a 3-3 deadlock and Mike Richards added a shorthanded, empty-net goal with 1:38 left. Richards also scored the game's first goal 54 seconds into the second period.
Simon Gagne and Slava Voynov produced the other Los Angeles goals, the first one shorthanded and the second one on the power play.