The poll by MDA consulting gave Rousseff 45.5 percent to 44.5 for Neves, a Social Democrat who is mounting a stiff challenge for the presidency of the South American giant in yesterday's run-off elections.
Discounting for blank and spoiled ballots, the poll found that Rousseff had a 50.5 to 49.5 percent lead.
A 2.2 percent margin for error meant the candidates remain in a technical tie with Rousseff pulling marginally ahead, having trailed Neves by a two-percent margin in polling last week.
But a number of parties have since thrown their support behind the challenger, including environmentalist Marina Silva, whom came in third in the first round.
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The latest poll, commissioned by the National Transport Confederation (CNT), showed 46.7 percent of respondents believed that former senator and Minas Gerais state governor Neves, 54, would win the election to 42.5 for Rousseff.
Rousseff has a slightly higher proportion of die-hard backers, however, with 38.1 percent saying she was the only candidate they would consider voting for -- compared to 34.4 percent who felt the same way about Neves.
For the poll, MDA interviewed 2002 people October 18 and 19 in 137 municipalities.