Kyle Clifford, Tyler Toffoli and Jeff Carter scored during a dominant first period, while Kopitar added his milestone goal in the third period of the Kings’ sixth win in nine games since mid-December.
Quick made 16 saves in his 51st career shutout, fifth-most among active goalies. The veteran netminder made a handful of big stops and combined with his defence to end the five-game scoring streaks of Edmonton stars Connor McDavid and Leon Draisaitl.
Mikko Koskinen yielded three goals on eight Kings shots before Cam Talbot replaced him in the first period for the Oilers, who have lost seven of eight.
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All-star Drew Doughty had two early assists for the Kings, who are on their first sustained stretch of strong play after languishing at the bottom of the league for much of the season.
With these two points, Los Angeles moved above Ottawa, Philadelphia and St. Louis while pulling even at the bottom of the Pacific Division with Arizona, albeit with more games played. They’re small but vital movements for the Kings after a dismal first half of the season that included the firing of coach John Stevens.
The Kings ranked 30th in the 31-team NHL with only 22 first-period goals before they got three more past the Oilers, who snapped a six-game skid in their last game.
Clifford put the Kings up just 3:15 in when he took a pass at mid-ice, skated around Caleb Jones and flipped in his sixth goal. The two-time Stanley Cup winner is already just one off his career high in goals.
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Toffoli scored after Doughty kept an Oilers turnover in the zone and set up the forward for only his second goal in 25 games.
Carter then chased Koskinen with his eighth goal of the season, picking the top corner on a rush when two Oilers failed to pressure the high-scoring forward.
The poor first period was a rerun for the Oilers, who also struggled early against Arizona on Wednesday before rallying to win.
Kopitar wrapped it up with his 10th goal of the season. The captain is the fifth player to score 300 goals for the Kings, joining Luc Robitaille (557), Marcel Dionne (550), Dave Taylor (431) and Bernie Nicholls (327).