Draisaitl scored his 49th goal of the season, and Mikko Koskinen made 38 saves for the Oilers (38-25-5), who trail the Kings by one point for second place in the Pacific Division.
"We won the game, and for us, that was the important thing," Edmonton coach Jay Woodcroft said. "It was a whatever-it-takes attitude. When you're not feeling 100 percent, the counterthrust to that is doing whatever it takes to get the two points, and it's a full credit to the people in the locker room who found a way and did whatever it took."
Alexander Edler and Carl Grundstrom each had a goal and assist for Los Angeles (36-23-10), which has lost its past two games. Jonathan Quick made 30 saves.
"I thought out guys did a good job, they were prepared for it, it's going to be that way from now until the end of the season," Kings coach Todd McLellan said. "But the group we have playing right now did a real good job tonight. We had to scratch and claw to come back. It's disappointing we didn't get the point when the shootout starts, but as far as the rest of the game, and finding guys to contribute, I thought we did a real good job."
Draisaitl and McDavid scored in the shootout. Viktor Arvidsson and Anze Kopitar failed to score against Koskinen.