Suzuki had two assists, and Carey Price made 14 saves for the Canadiens, the No. 4 seed from the Scotia North Division, who have won seven straight games and will play the Colorado Avalanche or Vegas Golden Knights in the Stanley Cup Semifinals.
"Obviously, we're excited about the opportunity, but we've got a lot of work ahead of us," Price said.
Montreal's winning streak is its longest in the playoffs since 1993, when it won 11 straight during a run to its most recent Stanley Cup championship.
"We can write our own story," Canadiens coach Dominique Ducharme said. "That's what we want to do."
Logan Stanley scored twice, and Connor Hellebuyck made 39 saves for the Jets, the No. 3 seed, who never led in the series.
"We just couldn't get the first goal," Winnipeg captain Blake Wheeler said. "We just couldn't do it all series, and that plays right into their hands, especially their top four defensemen. They're big and heavy and they do a great job of just clearing pucks and throwing them out of the zone."
The Canadiens have not trailed since Game 4 in the Stanley Cup First Round against the Toronto Maple Leafs, a series they won in seven games. Their streak of 437:53 is the second-longest in Stanley Cup Playoff history, behind the streak of 488:38 they set in 1960.
"They're playing at a really high level right now," Wheeler said. "You just have to give them all the credit."