Draisaitl is second in the NHL behind McDavid with 75 points (26 goals, 49 assists).
"He set me up twice," Draisaitl said. "It's two nice passes, [I] just had to make sure I bear down a little. Obviously, this time right now is about our team continuing to find our game, getting better every night, [but] on the side it's obviously about him trying to reach [100 points]."
Evan Bouchard, who played for the first time since March 1, scored on the power play at 19:13 to give Edmonton a 3-1 lead.
"It was a great feeling," Bouchard said. "You're working really hard off the ice, coaches are keeping us in shape, so to finally get back in a game was a good feeling."
Darnell Nurse scored on a 2-on-1 at 14:53 of the third period for the 4-1 final.
The Canucks outshot the Oilers 17-6 in the third.
"Obviously the last five minutes of the second cost us. A couple penalties, a couple turnovers, a missed change and it's 3-1," Vancouver coach Travis Green said. "I loved our third. If we had a little puck luck, we would have come back in the third."
NOTES: The Oilers were 2-for-3 on the power play; the Canucks went 0-for-4. … Bouchard had two shots on goal in 20:13 of ice time. … Edmonton center Kyle Turris played 11:01 in his first game since April 8. … Canucks defenseman Jack Rathbone made his NHL debut and had one shot on goal in 12:04. … Vancouver forward Tanner Pearson played his 500th NHL game.