Jayme de Almeida Filho's side secured the cup for the first time since 2006, completing a 3-1 aggregate win in Rio de Janeiro.
Elias and Hernane scored dramatic late goalsm while both sides had a man sent off as Flamengo left-back Andre Santos and Atletico PR substitute Ciro saw red.
Flamengo's third win puts them equal second alongside Corinthians for most Copa do Brasil crowns, one behind Gremio and Cruzeiro.
It also secures their place in the 2014 Copa Libertadores.
They needed until the 88th minute to go ahead in the tie for the first time thanks to Elias.
Paulinho turned his marker on the side of the area to get to the by-line before cutting back for the former Atletico Madrid attacker to place into the bottom corner.
Santos and Cirio, who was introduced in the 73rd minute, both saw red soon after before Flamengo sealed victory.
Luiz Antonio set up Hernane in the fifth minute of additional time to wrap up the hosts' win.
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