The former Brazil coach had to endure chants of "Goodbye Dunga" as his side, playing almost the entire second half with 10 men, lost for the second time in four days.
In other matches on Sunday, former world player of the year Ronaldinho inspired South American champions Atletico Mineiro to a 2-1 win over Vasco da Gama while Sao Paulo were beaten by a freak goal at Goias.
Internacional, fifth with 34 points from 23 games, left themselves an uphill struggle after defender Indio was sent off in the 48th minute for clashing with an opponent.
They managed to hold out until the 85th minute when Wanderson scored a breakaway goal to give relegation-threatened Portuguesa their first away win of the championship.
"We will stay together until the end of the year, the team staff will be maintained," club president Giovanni Luigi told Radio Bandeirantes, saying there was no question of Dunga being fired.
"It was our worst game of the year and we know that," Dunga told reporters.
Dunga was insulted with chants of "donkey, donkey" during a previous home game but shrugged it off by praising donkeys as "hard-working animals."
Ronaldinho set Mineiro on their way with a back-heeled pass for Fernandinho to open the scoring in the second minute before his free kick was deflected into his own net by Rafael Vaz in the 18th.
Dakson pulled one back for Vasco in the 73rd minute with a shot which went through the legs of Mineiro goalkeeper Victor.
Sao Paulo goalkeeper Rogerio Ceni was left cursing his luck when a 30 metre free kick from Rodrigo struck the post, hit him on the back and flew into the goal to give Goias a 1-0 win.
Leaders Cruzeiro (50 points) drew 0-0 at Corinthians and moved eight points clear of second-placed Botafogo, who lost 2-1 at home to Bahia.