Cruzeiro were in 11th place when the championship resumed in July after the World Cup recess.
With nine matches to go, Cruzeiro have 54 points, Flu 52 and Corinthians, who were upset 4-3 at home by Atletico Goianiense and have gone five matches without a win, on 49.
The defeat prompted Corinthians coach Adilson Batista to hand in his resignation.
"After the defeat by Atletico-GO at the Pacaembu this Sunday, Corinthians coach Adilson Batista handed in his resignation," the club quoted football director Mario Gobbi as telling reporters.
"Adilson Batista told us he understood he should leave the path clear (for another coach). He didn't want to prejudice the team that is fighting for the title."
Adilson, who steered Cruzeiro to the Libertadores Cup final last year, took charge of Corinthians in July when Mano Menezes left to take on the Brazil team following the departure of World Cup coach Dunga.
He presided over seven wins and six defeats in 17 matches.
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Cruzeiro, who could emulate Flamengo whose late surge won them the 2009 title, scored the only goal in the 15th minute.
Striker Wellington Paulista, back from a six-game absence due to a thigh injury, turned in a cross from the right by Argentine playmaker Walter Montillo.
"Now we must maintain the same rhythm for nine more games, starting with Gremio (next Sunday), which will be (like) another final," coach Cuca said.
Fluminense, who have not won in three matches, lost midfielder Deco during the first half with a thigh injury.
Corinthians went in front with a goal by central defender Leandro Castan and looked set for an easy win against relegation threatened Goianiense.
The visitors, however, responded with goals by Juninho, Gilson and Marcao, who put them 4-1 up after Castan was sent off for a bad tackle 12 minutes into the second half.
Corinthians began a fight-back with Williams Morais scoring in the 71st and Thiago Heleno three minutes from the final whistle but ran out of time.
"We started out winning but we can't offer counter-attacks to a team fighting against relegation," defender Chicao told reporters. "We're going to sit down and talk, these errors that are happening mustn't happen."
