Mike Richards, Drew Doughty and Alec Martinez also scored to help the Kings jump from eighth place to the third seed in the Western Conference.
Jonathan Quick made 13 saves, allowing only Jordan Eberle's power-play goal.
Los Angeles scored on its first shot of the game when Dwight King took a long shot that Kopitar tipped through Nikolai Khabibulin's legs at 52 seconds for his 25th goal.
Edmonton countered at 1:34 on a power play when Eberle snapped a shot from the right faceoff dot that went just inside of the post past Quick. Eberle has 33 goals this season. Rookie Ryan Nugent-Hopkins picked up an assist for his 50th point.
The Kings made it 2-1 midway through the first on Richard's short-handed breakaway. Jeff Petry missed the puck at the point on an Edmonton power play, and Richards sped away and beat Khabibulin with a backhander.
The Kings took a 3-1 lead 6:44 into the second period when Doughty's power-play point shot hit a defender's and deflected past Khabibulin. Martinez scored in the third period.
Notes: It was the third of four meetings between the teams. They will play again in Los Angeles on Monday night. Edmonton won the first two games. ... The Oilers recalled forward Magnus Paajarvi from Oklahoma City of the American Hockey League, but had to send him back after being informed they had exceeded the number of call-ups allowed after the trade deadline.