Santos defeated Fluminense 1-0 on Sunday to keep the 2012 Serie A champions on 42 points and just a spot above the relegation zone, as Coritiba and Vasco da Gama both made significant ground on Dorival Junior's team.
Coritiba snagged a point with a scoreless draw away to Internacional to sit behind Fluminense on games won, while Vasco moved up to 41 points with an impressive 2-1 victory over recently crowned champions Cruzeiro.
Santos overcame Fluminense with a well-worked goal in the 65th minute with Thiago Ribeiro tapping in Arouca's low cross.
In Rio de Janeiro on Saturday, Thalles Lima opened the scoring for Vasco after just two minutes before Edmilson doubled the home side's lead in the 33rd minute.
While Paulao pulled a goal back for Cruzeiro in the second half, the visitors were unable to avoid their first defeat in six matches, while Vasco gave their chances of Serie A survival a significant boost.
With two rounds remaining, Criciuma (43 points), Portuguesa (44) and Bahia (45) could also be dragged into the relegation battle.
Coritiba face the toughest finish to the Brazilian league season of the six teams between 13th and 18th on the table.
The Parana-based club have games against top-10 clubs Botafogo and Sao Paulo, while Vasco take on bottom-placed side Nautico plus second-placed Atletico Paranaense and Fluminense must play Atletico Mineiro (sixth) and Bahia (13th).
Criciuma face Sao Paulo and Botafogo, Portuguesa take on Ponte Preta and Gremio, while Bahia visit Cruzeiro before hosting Fluminense in the final round.
At the other end of the table, Atletico PR moved into the Copa Libertadores positions with a 6-1 thrashing of Nautico.
Atletico PR moved to 61 points and into second spot as Gremio slipped to third following a 1-1 draw away to Ponte Preta and Goias fell to fourth - which only sends a club into the qualifying rounds of the Copa Libertadores - after they lost 4-1 to Atletico Mineiro.
In other results, Criciuma drew 1-1 with Vitoria, Flamengo defeated Corinthians 1-0, Sao Paulo drew 1-1 with Botafogo and Bahia defeated Portuguesa 1-0.
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