Mikko Koskinen made 35 saves for Edmonton. On Wednesday, he was pulled and replaced by Mike Smith after allowing three goals on 12 shots in a 5-2 loss to the Ottawa Senators.
"I felt pretty good, like the team did in front of me," Koskinen said. "They did a really good job. Most of the shots came from outside and it was a big game for us. The game before, against Ottawa, wasn't good enough. Again we had a bounce-back game, but now we need to be sure we don't need to have those bounce-back games all over again."
Draisaitl scored at 11:02 of the first period to give the Oilers a 1-0 lead. His centering pass hit the skate of Kings defenseman Drew Doughty and deflected past Quick.
Edmonton has the No. 1 power play in the NHL, scoring on 32.2 percent of its opportunities (29-for-90).
"They get a lucky one off the foot on the power play and then they picked us apart for one too," Los Angeles coach Todd McLellan said. "But after that, we kept that team to 15 even-strength shots, and a lot of it was from the outside. So we're happy with the effort, we're disappointed in the result."
Los Angeles appeared to tie the game when Lizotte scored on a rebound at 14:05. The Oilers used their coach's challenge and it was determined Lizotte was offside when Adrian Kempe gained the zone.
"I knew it was close," Lizotte said. "When you drag your foot, you're not sure where the line is exactly. I knew it was going to be close. Even when I scored, I knew they were going to review it, and sure enough, it was a centimeter or two. It was real close."
Edmonton increased its lead to 2-0 at 14:46 when Alex Chiasson redirected a centering pass from Connor McDavid.
"With our lineup the way it is right now (with injuries), we're trying to grind out some points and that is what we did tonight," Oilers coach Dave Tippett said. "We gave some people some minutes who are more grind-mode and who dig in. We knew we needed a tight, hard-checking game just to get us back set in the right direction and we got that tonight."