If Neves does come in second in Sunday's first-round vote, leftist incumbent Rousseff would defeat him in the second-round runoff by 46.0 percent against 40.8 percent for Neves, according to the survey by polling firm MDA.
For the first round, support for leftist incumbent Rousseff was unchanged at 40.6 percent, while Neves has gained 4 percentage points from the previous MDA poll and moved into second place with 24 percent, ahead of Silva who has fallen almost 4 percentage points and is now third with 21.4 percent.
The gap between Neves and Silva is within the margin of error of the poll, but MDA said the trend was firm because the proportion of voters saying they would never vote for Neves had come down markedly.
The polling firm projects that the presidential election will be decided in a runoff between Rousseff and Neves.
Polls by bigger research firms Datafolha and Ibope that are more closely watched will be released later on Saturday.
If no candidate wins an outright majority as expected in the first round on Sunday (local time), the election will be go to a runoff between the top two vote-winners on October 26.
Silva, a popular anti-establishment figure, saw a dramatic surge in support when she entered the race after the death of her party's original candidate Eduardo Campos in a plane crash in August. Just one month ago, she was seen as the favorite to defeat Rousseff and end 12 years of Workers' Party rule in Latin America's largest nation.
But an aggressive media blitz by the Rousseff campaign has undermined her popularity by questioning her ability to govern Brazil without the backing of the traditional parties and painting her as the candidate of a financial elite determined to undo popular social welfare programs.
Neves, a senator and former state governor with a solid track record has risen steadily in the polls as Silva declined.
The number of voters who say they would never vote for Neves has fallen to 37 percent from 42 percent in a previous poll five days ago, while Silva's rejection rate has risen gradually and is now the same as Rousseff's, at about 42 percent.
The MDA poll commissioned by the transport industry lobby CNT surveyed 2,002 people between Thursday and Friday and has a margin of error of plus or minus 2.2 percentage points.
