Draisaitl, who had the secondary assist, received a penalty for unsportsmanlike conduct after the goal.
Kempe quickly tied it 2-2 at 9:40 on the power play, scoring on a slap shot after Viktor Arvidsson's stretch pass caromed off the boards behind the net and back to the right circle.
"Obviously anytime you're in the box, you're not putting pressure on the other team," Oilers coach Jay Woodcroft said. "We've liked the way we've played the game. In the end, we feel we're doing a lot of really good things that are putting hard miles on that team.
"We feel good about our game. Certainly, we can clean up some of the penalties. In the end, the score sheet would tell you we had four power plays, they had five."
Los Angeles was 2-for-5 on the power play; Edmonton was 2-for-4.
"It's breaks here and there, it's little calls here and there, and we haven't seem to be getting any of the bounces," McDavid said. "We had our looks, we had our chances, and they found a way to get a power play and they score in overtime."
NOTES: McDavid has 23 career playoff goals, passing Ryan Smyth (22) for eighth in Oilers history. … Draisaitl has 30 career points (10 goals, 20 assists) in 20 road playoff games, becoming the fourth player in NHL history to do so. Wayne Gretzky needed 13 road games to reach the mark, followed by Mario Lemieux (16) and Peter Stastny (19).