Jesperi Kotkaniemi gave the Canadiens a 1-0 lead in their first game since March 20, and Carey Price made 17 saves for his 49th NHL shutout, his first this season.
Artturi Lehkonen and Brendan Gallagher each had a goal and an assist for Montreal (15-8-9), which is 4-0-2 in its past six home games.
"It was a really good start for the team," Canadiens forward Paul Byron said. "Scoring those two goals gave us a lot of energy. Every player had a good game and it was a great team effort."
Montreal had four home games postponed after Kotkaniemi and Joel Armia were placed on the NHL COVID-19 protocol list March 22. The Canadiens were 2-0-2 heading into the pause.
"We knew we were going to be fresh, but we just harped on the little things and keep it simple, especially early on trying to get back into it," Canadiens captain Shea Weber said.
Connor McDavid had an 11-game point streak end, and Mikko Koskinen made 28 saves for Edmonton (22-14-1), which was 1-1-1 in a four-day span.
"We didn't start very well, we didn't play very well, and we didn't end very well," Oilers coach Dave Tippett said. "That's about it."
Edmonton played three games on a 10-day road trip that was reduced from five games. The Oilers lost at the Toronto Maple Leafs 4-3 in overtime Saturday and defeated them 3-2 in overtime Monday.
"It's obviously not an ideal situation here," McDavid said. "I mean, this has been one of the longest road trips I think I've ever been on and we played three games. So lots of sitting around, doing nothing. I think overall I liked our two games in Toronto and didn't like our one here tonight."
McDavid had a goal at 13:55 of the second period disallowed on a successful challenge by Montreal. Video review determined Jesse Puljujarvi was offside, and the clock was reset to 13:51.
Edmonton challenged but did not reverse Kotkaniemi's goal on the first shot of the game.
Lehkonen made it 2-0 when he scored on a backhand at 3:23 of the first period.
