Palmeiras were frustrated at home by Gremio, who played the last 10 minutes with 10 men after defender Rever went off injured following a clash of heads and their three substitutes already on the pitch. Rever was reported to be out of danger.
Playmaker Cleiton Xavier put Palmeiras ahead after half an hour with a header from Wendel's cross but Gremio equalised within three minutes with a low shot by Argentine striker Maxi Lopez.
"Sometimes it's easier to play away when your opponents go out to attack, than at home," Palmeiras captain and former Brazil keeper Marcos said.
Cruzeiro, flying high earlier in the season as they made their way to the Libertadores Cup final, have slumped since losing to Argentina's Estudiantes in the South American title decider last month.
Paranaense's Bruno Costa was sent off after 18 minutes, before Cruzeiro midfielder Bernardo was dismissed at the end of the first half and striker Kleber followed in the 70th minute.
Jorge Wagner and Washington scored in the last seven minutes of the first half to turn the match Sao Paulo's way and Dagoberto added the third, with his fourth goal in three games.
