Striker Leandro Damiao scored twice and Rafael Moura, Andres D'Alessandro and Gabriel shared the other goals as Inter overcame a difficult rain-sodden pitch.
They will meet the eventual winners of the second stage, still to be played, in the final.
Dunga, who captained Brazil's 1994 World Cup-winning side, was appointed in December for his first coaching job since he led Brazil to the quarter-finals of the 2010 World Cup.
Ten-man Sao Paulo overcame a red card for central defender Lucio to draw their derby 0-0 with Palmeiras and stay top of the Paulista championship's qualifying stage.
Dutchman Clarence Seedorf was involved in the only goal, scored by Lucas, as Botafogo beat Vasco da Gama 1-0 to win the first stage of Rio de Janeiro's Carioca championship.
