The Lightning clinched the best-of-seven series 4-1 in front of a packed arena to end a magical run by Montreal, who were ice hockey-mad Canada's latest hope of ending the country's longest Stanley Cup drought.
No Canada-based team has won the Cup since Montreal in 1993, a national embarrassment for hockey-mad Canadians.
Unlike last year, when Tampa Bay won the Cup without fans present inside the NHL's biosecure bubble in Edmonton, they did not squander a chance to close out the series in front of their boisterous fans.
"To do this in front of our fans and our family, we didn't get a chance to do that last year," said Lightning captain Steven Stamkos. "That was huge motivation for this group.
"It doesn't take anything away from last year but to do it again is just validation into history. This group accomplished something that not many people though could happen."
Tampa Bay scored the game's only goal with under seven minutes left in the second period when David Savard found rookie Ross Colton at the top of the crease with a tape-to-tape pass that slid under the stick of Montreal defenseman Ben Chiarot.
From there Andrei Vasilevskiy stood tall in the Tampa Bay net and finished the game with 22 saves for his fifth shutout of the 2021 postseason and fourth in a series-clinching game.
Vasilevskiy was awarded the Conn Smythe Trophy as the most valuable player of the playoffs.
The result ended an unexpected playoff run by an upstart Montreal team that defied the odds all season despite injuries, a COVID-19 outbreak and lacklustre regular season that left them a 50-to-1 longshot when the playoffs began in mid-May.
Montreal, who rode a hot goalie in Carey Price across three playoff rounds to reach the Stanley Cup final, had staved off elimination four times in the postseason but they lacked the offensive punch to keep their Cinderella run alive. Reporting by Frank Pingue in Toronto; Editing by Muralikumar Anantharaman, Robert Birsel