The Kings have won four straight and are 8-1-1 in their past 10 games. They moved out of a tie with Nashville and remained one point behind fourth-place Phoenix in the Western Conference.
"For the most part we gave up few chances," Brown said. "[Oilers rookie Jordan] Eberle had a good one in the third.
"Even with [Kopitar and Williams] in the lineup, our success has been in the defensive zone."
But even with a strong defense, goals will need to come from somewhere. Former Oilers forward Dustin Penner admits he feels pressure to contribute more than he has since his deadline-day trade.
"Everybody should have a bit more pressure on them," he said. "When you lose two guys like that, as a team you have to play better offensively. We are pretty sound defensively and in net but it looks like we will have to score by committee now."
The Oilers (23-42-11) have lost 10 straight, their worst skid since a 13-game slide last season.
"We didn't do a great job keeping the pace in the first period," Oilers coach Tom Renney said. "We needed to be better, and had we done that the outcome could have been a little bit different. We certainly gave it a good try at the end."
Edmonton's Nikolai Khabibulin was the busier of the two goalies during the scoreless first period. Khabibulin made 18 saves, the best of which was a partial breakaway stop on Kings captain Brown.
Los Angeles used the same combination to go up 2-0 with five minutes remaining in the second. Lewis stripped Jason Strudwick of the puck and fed it in front to a streaking Brown for his second of the game.
Bernier had his biggest save eight minutes into the third period when he made a quick glove stop on a shot from the slot by Jordan Eberle.
Edmonton came close again with four minutes left when rookie Teemu Hartikainen rattled a puck off the post.
|Dustin Brown beats Nikolai Khabibulin on the short side in the second period, during which he scores both of his goals. (AP)|
|Los Angeles (44-26-6) «||0||2||0||2|
Save Pct.: 1.000
|05:11||- Dustin Brown (27), Wrist Shot. Assist: Lewis, Smyth|
|14:56||- Dustin Brown (28), Snap Shot. Assist: Lewis|
|12.0||Cogliano, 2 min, Tripping|
|10:04||Smid, 2 min, Hooking|
|12:11||Gilbert, 2 min, Hooking|
|13:30||Brown, 2 min, Holding the Stick|
|16:21||Handzus, 2 min, Tripping|
|10:23||Jones, 2 min, Hooking|
|Shots On Goal|
|Attendance - 16839|
|Referees - Gord Dwyer, Chris Lee|
|Linesmen - Lonnie Cameron, Bryan Pancich|