Corinthians beaten ahead of Club World Cup trip
It was also a bad day for Brazilian champions Fluminense, crowned with three matches to spare three weeks ago but beaten 2-1 by Vasco da Gama in a match played mainly by their reserves in a nearly empty Engenhao in Rio.
Sport became the fourth and last team relegated after they lost 1-0 away to Nautico in the Recife derby, joining already condemned Palmeiras, Goianiense and Figueirense.
Gremio also had an unhappy farewell to their Olimpico stadium, to be demolished after 58 years' service, in a poor 0-0 draw with Internacional in the Porto Alegre derby.
The result allowed Atletico Mineiro to move above them into second place after a 3-2 win over Cruzeiro in the Belo Horizonte derby, putting them directly into the group stage of next year's South American Libertadores Cup.
Third-placed Gremio, who failed to beat an Inter side down to nine men for the final half hour, will have to win a preliminary round tie to qualify for the group phase, as will fourth-placed Sao Paulo.
Goalkeeper Muriel was sent off four minutes after halftime and Brazil striker Leandro Damiao was also dismissed on the hour.
The club have built a new stadium, considered the most modern in Brazil, which they will occupy from next season.
The Olimpico's goodbye party was marred by coach Vardelei Luxemburgo being sent to the stands for entering the field of play during an argument with the referee and having to be removed by police.
Inter's caretaker coach Osmar Loss was also involved in a scuffle and shoved by Gremio defender Saimon, who earned a red card, in added time when a flare landed close to an Inter official.
Gremio fans, some in tears, tried to tear out seats as keepsakes of a venue where their club won the Libertadores Cup final twice in 1983 and 1995.