Connor McDavid had three assists, Kailer Yamamoto and Kris Russell each had a goal and assist, and Mike Smith made 34 saves for the Oilers (46-26-6), who have won four straight.
Edmonton is four points ahead of the Los Angeles Kings for second in the Pacific Division.
"It was a good team win, it's great to clinch the playoffs here at home," Kane said. "I thought in the first period we came in a little flat, we didn't do what we talked about heading into the game, but we got off to a strong start in the second and carried the momentum all the way through."
Valeri Nichushkin scored two goals and Darcy Kuemper made 21 saves for the Avalanche (55-17-6), who have lost three straight. The Central Division champions have clinched first in the Western Conference and are two points behind the Florida Panthers for No. 1 in the NHL.
"Yeah, it's definitely concerning, we're shooting ourselves in the foot a lot of the time," Avalanche center Nathan MacKinnon said. "I feel like a lot of those goals are preventable -- most of them -- I can think of three. It doesn't matter who's in the lineup, we can be good with the puck, all of us are NHL-caliber players, we can make smart decisions. Regardless of the guys we're missing and regardless of the standings, we're trying to get better, and we need to definitely improve."