Leon Draisaitl added a goal and two assists and Darnell Nurse also scored for the Oilers in the opener for both teams. Jack Campbell made 33 saves.
''It wasn't according to anyone's script, for sure,'' said Edmonton head coach Jay Woodcroft. ''I don't think we were sharp. I don't think we were in sync early. We found a way to win the game, that's a really good sign, but we can be better.''
Elias Pettersson, J.T. Miller and Andrei Kuzmenko - in his NHL debut - scored for the Canucks. Thatcher Demko stopped 20 shots.
Pettersson and Miller scored in an early 51-second span and Kuzmenko made it 3-0 39 seconds into the second on a power play. He's the first player in Canucks history to score a power-play goal in his debut.
''That was pretty disappointing, I thought we came out pretty good in the first and special teams kind of cost us the game,'' said Canucks defenseman Oliver Ekman-Larsson. ''The power play wasn't good enough and we couldn't keep the puck out of our net on the (penalty kill).''
Edmonton got on the board 4:12 into the second when Draisaitl took a deflected pass at the side of the net and slammed it past Demko on a power play.
The Oilers pulled within a goal with another power-play goal with 5:59 left in the second on a three-way passing play from Zach Hyman to Draisaitl and then to McDavid.
''It was just not a good start for our group. It was the first game and maybe there was a little bit of jitters,'' McDavid said. ''It is not going to be perfect every night. You are not going to have the game you want every night and sometimes you get a win with your `B' or `C' game. It was certainly not our `A' game to start, but we found a way to get our legs going and get ourselves back in it.''
Edmonton pulled even with 41 seconds left in the period on a 2-on-1 short-handed break as Draisaitl fed it across to Nurse, who beat Demko with a one-timer.
The Oilers took the lead with 4:59 left in the third period with McDavid orchestrating a give-and-go with Hyman before depositing his own rebound past Demko. It was McDavid's 700th career point, making him the sixth-fastest player to hit the mark in 488 games.
McDavid completed the hat trick with 25 seconds left when Evander Kane dropped it back to him for an empty-net power-play goal.
More AP NHL: https://apnews.com/hub/NHL and https://twitter.com/AP-Sports
Copyright 2023 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.