The defending champions lead 1-0 at the first intermission after Cernak, a defenseman playing in his 46th career postseason game, beat Carey Price from the slot off a pass from Ondrej Palat at 6:19 of the opening period.
Playoff goals leader Brayden Point also assisted for Tampa Bay, which has never won Game 1 of a Stanley Cup Final.
Price is making his Stanley Cup Final debut in his 14th season with the Canadiens. He is the first goaltender in league history to win more than 400 regular-season and playoff games combined before appearing in a Cup Final.
Meanwhile, center Jake Evans is in the Canadiens lineup after missing nine games due to a concussion.
Montreal forward Joel Armia was scratched, however, after being cleared from COVID-19 protocol and being flown by private jet to Florida earlier in the day.
The Lightning are in the Stanley Cup Final for the third time since 2015. The Canadiens have won a NHL-record 24 championships, though none since 1993 — Tampa Bay’s first season in the league and the last time Montreal played on hockey’s grandest stage.
Tampa Bay eliminated the Florida Panthers, Carolina Hurricanes and New York Islanders along the way, with Vezina Trophy favorite Andrei Vasilevskiy extending an impressive streak of shutouts in series-clinching victories to four dating to last year Cup Final against Dallas.
Montreal had the worst record among 16 playoff qualifiers this season, but with Price leading the way the Canadiens played superb defense in ousting the Toronto Maple Leafs, Winnipeg Jets and Vegas Golden Knights.
Vasilevskiy had five saves in the opening period. Price stopped six of seven shots he faced.
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