McDavid gave Edmonton a 1-0 lead on his first shift, 45 seconds into the first period when his shot hit the leg of Canucks defenseman Alexander Edler and went between Demko's pads.
Jesse Puljujarvi one-timed a pass from McDavid on a 3-on-1 to make it 2-0 at 6:53 of the second period.
J.T. Miller scored unassisted for Vancouver at 9:12 to make it 2-1, and Travis Boyd tied it 2-2 at 11:40 with a shot from the top of the right face-off circle.
"I did like our first, [but] I didn't think we moved our feet that well," Canucks coach Travis Green said. "But we hung in there, it was still 1-0 and we regrouped after the first, talked to our team [about] what we needed to do to be better, and they played a lot better in the second. We started to move our feet, got to the net and got some greasy goals and got ourselves back in the game."
Draisaitl gave the Oilers a 3-2 lead on the power play at 12:27 of the second period on a one-timer from James Neal, who took a drop pass from McDavid. It was Draisaitl's 500th NHL point.
"Obviously I'm proud of it, no question, but I'm planning on playing a few more years," Draisaitl said. "I think the fun years are still ahead here in Edmonton. [I'm] just fortunate and happy to be part of it and really excited for the next couple of years."