Connor McDavid and Tyler Ennis also scored in Edmonton's fourth consecutive win. Mike Smith had 30 saves.
''That win right there carries some weight to it,'' Smith said.
''We've scratched the surface now and now I think we've gained some confidence in how our team can play.''
The difference, Smith added, was how the Oilers withstood a late push by the Canucks.
''We kind of hunkered down and made sure they were going to have to make a real good play to beat us in that game,'' said Smith, who earned his fifth win of the season.
''Being here for the last couple years, I've been in games where that one slides away from us and gets away. And I think tonight, that was a great confidence builder for all of us.''
It's a result that could have some teachable moments going forward, according to Edmonton coach Dave Tippett.
''If we get another game like this, then there's a belief that we can do it again,'' he said. ''We came in here, we didn't play as well as we liked the first period, we got better as the game went on. We knew we were playing a desperate team that's trying to get back in the race.
''It's a huge two points for us. Now we have to kind of park that game and get ready for the next one, because their desperation level goes up.''
Bo Horvat, Tyler Myers and Elias Pettersson scored to help the Canucks build a 3-0 lead in the first period, but they were shut out for the rest of the night.
Kahun sparked the Oilers' comeback with goals late in the first and early in the third. McDavid tied it at 3 with his 13th goal 4:23 into the third, with this one coming on a power play. Ennis put Edmonton in front with his second of the season at 13:25.
Thatcher Demko made 25 saves for the Canucks, who have just two wins in their last 12 games.
Coach Travis Green said the Canucks got what they deserved.
''I didn't think we were as good tonight as we have been,'' Green said. ''Quite frankly, we had some individuals that didn't play good enough tonight.''
The teams play again in Vancouver on Thursday.
More AP NHL coverage: https://apnews.com/hub/NHL and https://twitter.com/AP-Sports
Copyright 2021 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.