The Brazilian giant had won the first leg in Buenos Aires 4-0 to have complete control of the tie coming in, but Lucas Pratto created some doubt with the opener in the 21st minute at Estadio do Maracana.
Pedro, who netted a hat-trick in the first leg, settled any nerves with an expert header from Everton Ribeiro's cross shortly prior to half-time to square the match up.
As the game opened up, Marinho thumped in a left-foot winner in the 68th minute, with Pedro's skill setting up the opportunity.
The Brazilians were denied a third goal in stoppage time after a VAR review, with Pablo's header from Marinho's cross deemed offside.
Flamengo will take on fellow Brazilian club Athletico Paranaense in the decider on October 29 in Guayaquil.
Athletico got past Palmeiras 3-2 on aggregate, after a 2-2 second-leg draw in Sao Paulo on Tuesday.
Flamengo will be chasing their third Copa, while Athletico are after their first, having been runners-up in 2005.