Argentinian striker German Cano gave Fluminense the lead with a goal in the 36th minute but in the second half Luis Advincula equalised for Jorge Almiron's side with a shot from outside the box.
Kennedy's unstoppable shot gave Fluminense the winner in extra time, though two minutes later the forward was sent off for excessive celebrations after receiving his second yellow card.
Before the end of the first half of extra time a brawl broke out between the players with Boca's Frank Fabra slapping Fluminense captain Nino for which he was sent off.
"I recovered the ball for my son Lorenzo. I can tell him now that I am champion of the Libertadores," said Cano, whose 13th goal this season in the competition was as many as the total scored by all of Boca's players combined.
"I want to dedicate this title to my family, the team, our director and the fans. It was a dream that we wanted to achieve since the first game," he added.
Fluminense's Fernando Diniz, who is also Brazil's interim coach, finally delivered the elusive trophy - the equivalent to Europe's Champions League - for a team who lost the 2008 final.
"We had a lot of chances today but in the end we failed to capitalise on the opportunity to take advantage of the extra man," said Boca goalkeeper Sergio Romero.
"I think we did a great cup (run), we thank the people and we regret not giving them a joy today."
Boca were aiming for a seventh Libertadores crown but have now lost their last three finals after defeats in 2012 and 2018.
