Connor McDavid scored on a breakaway with 2:18 remaining in overtime, but Montreal had already clinched the fourth berth in the Scotia North Division when it was guaranteed at least one point at the end of regulation after Artturi Lehkonen scored at 13:04 of the third period to tie it at 3-3.
"We had a tall task tonight, and it was great to see everybody just pushing so hard in the third period to try and get the equalizing goal," Canadiens forward Paul Byron said. "It was a great team effort."
McDavid had an assist for his sixth straight multipoint game for Edmonton (34-18-2), which clinched the No. 2 seed in the North on Saturday. Mikko Koskinen made 25 saves.
"You could definitely get a sense of their desperation," McDavid said. "But that's a great thing for us, to be able to play a team like this with their desperation, with their intensity level tonight. That's how it's going to be moving forward, so that was a good test for us, and good for us to keep our playoff mindset going."
Lehkonen and Jake Evans each had a goal and two assists, and Jake Allen made 31 saves for Montreal (24-21-10), which will make its second straight postseason appearance.
"We were pretty confident we were going to clinch this by either this game or the next game," Lehkonen said. "But now that we're done, we've just got to keep building on toward the end of the season."
Byron, who missed the previous nine games with a lower-body injury, had a goal and an assist, and his line combined for eight points while tasked with defending McDavid, who was on the ice for all three Montreal goals.
"I think all three of us, our line, was pretty excited for the challenge," Evans said. "Our line together has worked well in the past, and I think we like our speed, our grit, and how hard we are on the forecheck. So to get that opportunity, I was excited, I wasn't nervous, and I love those opportunities."