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.
The Gaucho championship, played in the southern state of Rio Grande do Sul, is one of a plethora of bafflingly complex regional tournaments which kick off the marathon Brazilian season.
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.
The former Brazil and Bayern Munich defender was dismissed for elbowing midfielder Jorge Valdivia early in the second half.
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.
