Gabriel Barbosa grabbed the decisive goal on the stroke of halftime, slotting home a fine cross from Everton Ribeiro at the back post.
The goal came just minutes after Athletico central defender Pedro Henrique was sent off after picking up a second yellow card for a late challenge on Ayrton Lucas.
Down to ten men for the remainder of the game, Athletico, coached by veteran former Brazil national team coach Luiz Felipe Scolari, struggled to create enough chances to mount a comeback.
The victory earns Rio club Flamengo their third Libertadores title following their successes in 1981 and 2019 and is the fourth straight year that a Brazilian team has been crowned champions of South American club football.
For the 73 year old Scolari, who is expected to retire from coaching at the end of the Brazilian domestic season in November, there was to be no fairytale end to his 40 year coaching career.
Scolari had been hoping for a third Libertadores title to add to those who won with Gremio in 1995 and Palmeiras in four years later.
Scolari may be noted for a cautious approach to the game but his side began positively in the mid-afternoon heat.
Flamengo's former Paris Saint Germain and Chelsea defender David Luiz was caught out early on by Vitinho who tested Santos with a near post drive as Athletico enjoyed some early pressure.
Moments later, a long throw into the Flamengo box caused confusion and Alex Santana blasted just over with a spectacular effort.
Although Flamengo gradually took a grip on the midfield, Athletico looked comfortable before Pedro Henrique's rash challenge changed the game.
Substitute Ayrton Lucas showed good pace as he burst down the left but the Paranaense defender's lunging challenge was slightly late and the referee's yellow card left his team a man down.
Before Scolari had even made a tactical substitution, Flamengo had taken advantage with Everton Ribeiro finding space after a swift exchange with Rodinei before delivering a perfect ball across the area which Barbosa pounced upon.
It was Barbosa's fourth goal in his third Libertadores final adding to the two he scored in the win over River Plate in 2019 and his effort in the 2-1 defeat to Palmeiras last season.
It was not until the latter stages of the game where Athletico put Flamengo under any real pressure but Pedro was off target with a close-ranger header and Santos did well to keep out a David Terans free-kick.
"We deserve to be champions," said Barbosa, "I'm so happy and now we have to celebrate a lot because we deserve it"
"On Monday we will invade Rio de Janeiro and we will have a big party. I thank the fans for their love," he added.
Barbosa's strike partner Pedro, voted player of the tournament, was ecstatic with the triumph.
"It's been a dream since I was a child. I was in the stands and I lived it on the field. To live this feeling is wonderful," he said.