The Kings outshot the Oilers 14-7 in the third.
"I didn't think we played particularly well in the third period," Edmonton coach Jay Woodcroft said. "There were moments in that period we would like to have back, and we could be better. In the end, they scored a 6-on-4 goal with 17 seconds or so to tie it up. That's disappointing, and we couldn't find the winner in overtime."
Draisaitl gave the Oilers a 1-0 lead at 6:57 of the first period with a shot from inside the left circle, and Bouchard made it 2-0 at 12:31 with a snap shot from the slot during a 5-on-3 power play.
"We played some good hockey for the most part," Draisaitl said. "It's not how we planned it. We obviously wanted to come out and win this game, but we didn't, so we've got to regroup and get ready for the next one."
NOTES: Los Angeles lost to Edmonton in seven games in the first round last season. … Oilers center Connor McDavid, who led the NHL in goals (64), assists (89) and points (153) during the regular season, was held without a point. He had a 16-game point streak to close out the regular season. … Kopitar is the first Kings player to have four points in a playoff game since Jeff Carter in Game 2 of the 2014 Western Conference Final. … Los Angeles defenseman Alexander Edler returned after missing the final five games of the regular season. He had two blocked shots in 18:01 of ice time. … Teams that take a 1-0 lead in a best-of-7 series have a series record of 503-232 (.684), including 4-4 in the first round last season. … Edmonton was 1-for-3 with the man-advantage after having the best power play in NHL history during the regular season (32.4 percent). Los Angeles, which was fourth on the power play during the regular season (25.3 percent), was 2-for-6.