J.T. Compher scored twice, and Mikko Rantanen, Nathan MacKinnon, and Gabriel Landeskog each had a goal and an assist for the Avalanche, the No. 1 seed in the Western Conference.
"I liked our checking game for the most part. We were unfortunate on a couple plays," Colorado coach Jared Bednar said. "It felt like when we made mistakes, they capitalized on them. We have to make less mistakes, but we did get unfortunate on a couple goals, in my opinion."
Darcy Kuemper made 13 saves before he left the game at 7:19 of the second period because of an upper-body injury. Pavel Francouz made 18 saves in relief.
Asked if Kuemper is day to day, Bednar said, "We'll see."
Game 2 of the best-of-7 series is here on Thursday.
"I have a lot of faith in Francouz]. So does our team," Bednar said. "So, having a guy like that is obviously key. See through the playoffs how many teams are onto their second goalie and some teams' third and trying to survive. You've got to have capable goaltending from more than one guy, and we have it."
***[RELATED: [Complete Avalanche vs. Oilers series coverage]*
Connor McDavid had a goal and two assists, and Evander Kane and Ryan Nugent-Hopkins each had a goal and an assist for the Oilers, the No. 2 seed in the Pacific Division.
"We scored six goals on their goaltending tandem tonight in their building. That should be enough to win the game," Edmonton coach Jay Woodcroft said. "For me, there are things we have to do in terms of preventing. Sometimes I think it's not about what you get, it's about what you've given up, and we gave up far too much tonight."
Mike Smith made allowed six goals on 25 shots before being replaced at 6:20 of the second. Mikko Koskinen made 20 saves in relief.
Smith was also pulled in Game 1 of the second round, when he allowed three goals on 10 shots in the first period of a 9-6 loss to the Calgary Flames on May 18.
"Obviously when you're giving up touchdowns in the last two series in Game 1, I think that's not a good sign," Smith said. "But I think it shows a lot of our team that when we're down, we're not out of the fight and continue to battle right to the end and play for each other."