After the Kings and Oilers finished overtime in a 1-1 deadlock, Mike Richards opened the tiebreaker with a shot over the glove of Edmonton goalie Richard Bachman, and Jordan Eberle responded with a tally against the Kings' Jonathan Quick.
Neither team scored in the second round. Kopitar sealed the victory in the third when his forehand shot got past Bachman.
Ryan Nugent-Hopkins missed on the Oilers' final try and the Kings claimed their fourth win in five games.
Richards scored in regulation and Quick turned aside 17-of-18 shots for Los Angeles.
Bachman, playing in his first game as an Oiler after being called up from the American Hockey League Saturday, stopped 47-of-48 shots.
Nail Yakupov scored Edmonton's only regulation goal.