Struggling champions Flamengo, meanwhile, named former Brazil midfielder Silas as their third coach of the season before conceding two goals in stoppage time to lose 2-1 away to Guarani.
Flu lead the championship with 37 points from 17 matches, three points more than Corinthians who beat Vitoria 2-1 in former Brazil striker Ronaldo's first appearance since the World Cup recess.
Santos and newly-crowned South American champions Internacional, who both have a game in hand, and Botafogo are joint third with 27 points.
Flamengo's sixth defeat in 17 matches left them 13th with 21 points, while Sao Paulo are 15th with 19.
Ceni equalised with a free-kick after former Portugal midfielder Deco had put Fluminense ahead with his first goal for the club in his third match since joining them from Chelsea.
Sao Paulo striker Fernandao made it 2-1 with a header before half-time but defender Leandro Euzebio headed Flu's equaliser on the hour.
PENALTY SAVE
Flu striker Washington could have scored a winner with a penalty for handball by Richarlyson but Ceni produced a brilliant diving save in the left corner of his goal.
"The important thing today was to add a point in this delicate moment we're going through. What least matters now is the individual," Ceni told reporters of the six-times Brazilian champions' plight.
"When we're winning and all's well we can even take the luxury of exalting personal records and achievements, but at this moment Sao Paulo need to be united to try and get out of this situation."
Flamengo looked set to mark the arrival of former Brazil midfielder Silas, sacked by Gremio three weeks ago and watching in the stands a few hours after his appointment, with a victory after a headed goal by defender Jean.
But Guarani, for whom Ricardo Xavier had missed a penalty, turned the result around in added time when Ailson knocked in a free-kick with his knee and Reinaldo struck the winner in the next attack.
Flamengo's executive director and former Brazil international Zico said he was confident Silas could turn the club around.
"He's a trainer from the new generation who has been doing a great job for a long while and can find what we want," Zico said.
"He likes attacking football and that fits well with Flamengo."
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