Jesse Puljujarvi had a goal and an assist, Tyson Barrie and Dominik Kahun also scored and Leon Draisaitl added two assists for Edmonton in the opener of a four straight games between the teams. Mikko Koskinen stopped 20 shots for his 12th win of the season.
''Your first goal every season is to play in the playoffs. That's step one and we've been able to do that,'' McDavid said. ''Now we just need to continue working on our game and pay attention to details and get ready for the playoffs.''
Edmonton sits second in the North Division, eight points behind Toronto. Vancouver remains at the bottom of the all-Canadian group with nine games to go.
Last year, the Chicago Blackhawks bounced the Oilers from the playoffs in a five-game play-in round series. It's an experience that's motivated the squad this year, McDavid said.
''Everyone left the bubble in a bad mood. No one felt great about where we were at, how that series went,'' he said.
This season, everyone in the locker room has done a good job of buying in and believing, he added, and on the ice, they've found ways to keep pucks out of the net.
''And offensively, I've been pretty good,'' said McDavid, who leads the NHL in scoring with 91 points (31 goals, 60 assists). ''So I think that's a recipe for a playoff team. And now it's up to us to make sure we're ready to go for Game One.''
Nate Schmidt, J.T. Miller and Brock Boeser scored for the Canucks, who lost their fifth straight. Braden Holtby had 27 saves.
''Obviously their top line was a big factor in the game,'' Vancouver coach Travis Green said. ''We made a couple mistakes on a couple of their goals but you're gonna make mistakes and they made us pay. I thought we had one line that had a really strong game, a couple lines that worked extremely hard, and didn't get rewarded, and we tried to push at the end.''
The teams meet again Tuesday night in Vancouver, before heading to Edmonton for two.
The Oilers held a 4-2 lead heading into the third period and refused to relent. The Canucks had a single shot on goal through the first 15 minutes of the period.
Vancouver pulled Holtby with 3:29 left on the clock and the move immediately paid off as Boeser sent a bullet soaring past Koskinen off a face-off draw. The right wing leads the Canucks in scoring with 38 points (18 goals, 20 assists).
McDavid sealed the score at 5-3, burying an empty-netter with 1:00 to go in the game.
Oilers coach Dave Tippett liked the way his group held on for the win.
''I thought we were pretty solid. We weren't giving up a lot,'' he said. ''We have to continue to improve in that area. It's not just checking. It's our play without the puck but also our play with the puck, the ability to make good plays, not turn the puck over at the wrong places on the ice and play in the offensive zone.''
Barrie gave Edmonton a 2-1 lead just 18 seconds into the second period. Holtby stopped a shot from Puljujarvi but couldn't corral the rebound. Barrie scooped up the puck at the top of the crease and quickly popped it in for his eighth goal of the season.
McDavid picked off a Canucks pass in the neutral zone, skated into Vancouver territory and blasted a shot at Holtby with about 3 1/2 minutes left in the period. The netminder initially seemed to make a glove save, but the puck trickled through and his attempt to dive backward and sweep it off the goal line was unsuccessful.
Just 41 seconds later, Vancouver pulled to 3-2 when Miller tucked a backhanded shot under Koskinen's outstretched glove from the top of the crease. It was Miller's 12th.
Kahun closed out the second period with a blast past Holtby, making it 4-2 for Edmonton with 44.1 seconds left on the clock.
The Oilers got an early lead after McDavid sent a slick pass to Puljujarvi across the slot. The Finnish forward fired a one timer past Holtby from the right face-off circle to give Edmonton a 1-0 lead 3:45 into the game. It was Puljujarvi's 13th goal.
The Canucks tied it before the end of the first, thanks to Schmidt's fifth goal of the season. The defenseman took advantage of a net-front screen by rookie Nils Hoglander and rifled a shot from the top of the left face-off circle, beating Koskinen on his blocker side.
The Canucks recalled D Jack Rathbone and C Tyler Graovac from the taxi squad earlier on Monday, moves aimed at filling spots on a team that's been rocked by injuries.
C Brandon Sutter (upper body) was the latest Vancouver player to go down with an injury, joining forwards Tyler Motte, Antoine Roussel, Jay Beagle and Elias Pettersson who were already out with various ailments.
The team also placed right-winger Jake Virtanen on leave on Saturday amid an investigation into allegations of sexual misconduct.
Oilers defenseman Darnell Nurse played his 400th NHL game.
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