The Rio de Janeiro club, however, are still not clear of the four-team drop zone despite a run of seven matches without defeat including four wins, because the battle at the bottom is as intense as that at the top.
Fluminense's arch-rivals Flamengo beat Atletico Mineiro 3-1 away to move into third place two points behind new leaders Sao Paulo and one below Palmeiras with four matches remaining.
Flamengo's Serbian midfielder Dejan Petkovic curled the ball in direct from a corner for the second time in five games to put his team ahead after 10 minutes at the Mineirao in Belo Horizonte.
Chilean midfielder Claudio Maldonado increased Flamengo's lead half an hour later and Brazil's Adriano secured the points with a header eight minutes from the end before Ricardinho pulled one back.
It was former Inter Milan striker Adriano's 18th goal, putting him level with Atletico's Diego Tardelli as joint top scorers in the championship.
Sao Paulo, who have won the title the last three years in a row, drew 1-1 with Gremio in midweek but Palmeiras have been unable to profit from other teams' slips in recent weeks with only one win in seven matches.
A crowd of nearly 70,000 at the Maracana watched Fluminense record their third successive win with a headed goal on the hour from striker Fred, who took his tally to eight in eight matches in all competitions.
Fluminense, Libertadores Cup finalists last year, have reached the semi-finals of the Copa Sudamericana, South America's equivalent of the Europa League.
"We've been on a knife edge for the last five, six games but we can't relax," said Cuca, the team's fifth coach this year.
"We have to press harder with each match but also we have to be humble."
