Alex Chiasson, Zack Kassian and Ryan Nugent-Hopkins scored, and Connor McDavid had two assists for Edmonton (30-30-7), which is seven points behind the Minnesota Wild for the second wild card into the Stanley Cup Playoffs from the Western Conference. Mikko Koskinen made 35 saves for his 20th win of the season.
"It probably wasn't our best 60 minutes, but guys that have been around in this league for a long time understand that sometimes you have to find a way to get two points," Chiasson said. "It seems like we've been able to do that lately. Obviously, our goaltending has been key. We were able to get off to a good start at home, something that we haven't done in the past."
WATCH: [All Canucks vs. Oilers highlights]
Jay Beagle and Alexander Edler scored, and Thatcher Demko made 31 saves for Vancouver (28-31-9), which is nine points behind Minnesota.
The Canucks fell behind 3-0 in the second game of a back-to-back after defeating the Toronto Maple Leafs 3-2 in overtime in Vancouver on Wednesday.
"We have to make sure that we don't allow ourselves to get down one or two in a game," Beagle said. "We have a lot of resiliency and a lot of heart and have a lot of guys who don't quit. But when you go down by three, it is tough, especially on a back-to-back on the road. We showed a lot of heart in never quitting."
Chiasson scored at 5:21 of the first period to give the Oilers a 1-0 lead. Kassian made it 2-0 at 14:07 when he tapped in centering pass from McDavid at the top of the crease.
"Any smart player knows to get [McDavid] the puck early, and that's what [Kassian] does," Edmonton coach Ken Hitchcock said. "He gets him the puck early, so he knows by the time he counts to four, it should be in Connor's hands. And he's really smart that way. That's an easy thing to say but a hard thing to do because you have all this space in front of you and you want to carry it, but he knows right now to give it up and knows that if he gives it up, he's going to get it back and be in good spots like he did on the goal."
Draisaitl had an assist on Kassian's goal and has nine goals and nine assists during the longest active point streak in the NHL.