Veteran forward German Cano opened the scoring for the Brazilians in the first half, sweeping home a first-time shot.
Luis Advincula equalised with a stunning strike from distance to take the game to extra time.
In the added period, substitute John Kennedy powered in the winner before he was sent off after a second booking.
The Brazilian forward, already on a yellow card, raced off to celebrate the historic strike in the crowd and was subsequently dismissed on his return to the pitch.
That left Fluminense needing to hold on with 10 men against six-time champions Boca Juniors, but the Argentines were also then reduced in number when Frank Fabra was dismissed for slapping Nino.
The Copa Libertadores final – South America’s equivalent of Europe’s Champions League final – can often be a sparky affair, but on the pitch this one took a while to get going, before it exploded into life in a drama-filled and tense extra time.
Kennedy’s explosive 18-yard finish for his goal was worthy of winning any final, as he powered an unstoppable drive into the back of the net.
That was a real blow to Boca’s hopes of taking the game to penalties and although they dominated possession, it was Fluminense who went closest to scoring again when Guga’s shot hit the post.
However they held firm until the referees’ final whistle which was met by huge celebrations on and off the pitch.
