Trailing by 10 points after the opening quarter, the Tigers piled on seven unanswered goals to tear the game open and roared on to a 16.12 (108) to 8.12 (60) victory in front of a festive crowd of 100,021 at the Melbourne Cricket Ground.
The Tigers' talismanic midfielder Dustin Martin capped his brilliant season by winning the Norm Smith medal as the most valuable player on the ground.
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The 26-year-old, who was awarded the Brownlow medal as the 'best and fairest' player of the season, finished with 28 possessions and two goals in Australian Rules football's showpiece match.
The Crows, bidding for their first championship since back-to-back titles in 1997-98, were the dominant side of the regular season and entered the match as the bookmakers' favourites.
But after starting brightly with four goals in the first quarter, they promptly crumbled under pressure, their forwards completely shut down by their opponents' superb defence.
"It's been an incredible year and I've just loved working alongside you all," Tigers captain Trent Cotchin told his team at the post-match trophy presentation.
A massive thank you to our fans and members. You deserve this.
The Damien Hardwick-coached Tigers won their first championship since Tony Jewell's side lifted the 1980 trophy with victory over the Collingwood Magpies.
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