The scoring in this one was started by the Canucks. Following a turnover, Alexander Burmistrov hit Jake Virtanen in front of the net with a pass and the Vancouver forwarded deposited it behind Cam Talbot at 12:53 of the opening frame.
The goal was Virtanen's fourth of the pre-season.
With 1.4 seconds left on the clock in the first, Draisaitl ripped a one-timer past Jacob Markstrom for the equalizer. Connor McDavid and Patrick Maroon each recorded assists on the tally, which was Draisaitl's second of exhibition play.
Edmonton led in shots 10-4 following the first period of action.
That McDavid to Draisaitl connection hooked up again at 7:48 of the second period. The goal came on a 5-on-3 power play for the Oilers. Mark Letestu recorded the second assist.
The lead didn't last long for Edmonton, however, as Markus Granlund buried one on a shorthanded breakaway just 21 seconds later to tie the game at 2-2.
"We would have liked to have been a little bit better tonight, but we did a lot of good things," said McDavid. "There are definitely some areas to improve on. We definitely need to sharpen up the power play and penalty kill and be a little bit stronger in the d-zone, but offensively I thought we had our chances. We just have to bear down."
The Canucks kept their special-teams momentum going at 12:41 of the middle frame. Loui Eriksson gloved the puck down to himself at the post and tapped in the go-ahead goal.
"We finally go on the power play, score, and then we give it right back to them. So that was a gift," said Oilers Head Coach Todd McLellan. "After that, it became pretty tight checking, there wasn't a lot of space out there and we weren't able to get the last one."
Midway through the third, Oilers forward Ryan Strome drew a slashing penalty to give Edmonton a much-needed power-play opportunity. The team's second unit piled on the pressure but couldn't beat Markstrom.
The Canucks nearly took a two-goal lead with less than five minutes to go, but the puck was tipped in with a high stick.
The Oilers had nine shots in the third period, but could not put the biscuit past Markstrom and so the Canucks held on to get the win.
"We'll put the whole exhibition season behind us now," said McLellan. "We have to get home and get prepared for Calgary. I think the competition level is going to go up a little bit more and we're going to have to take our game up a little bit more."