Rousseff had 35 percent of votes, compared to 24 percent for Senator Aecio Neves and 11 percent for former governor Eduardo Campos, according to the survey by Sensus polling firm.
Undecided voters and those who said they would spoil their ballots accounted for the remaining responses.
The Sensus result indicated a tighter race than a separate poll released earlier this week, which showed Rousseff leading Neves by 15 percentage points.
Brazil's stock market advanced 2.6 percent on Friday as investors anticipated the Sensus poll would show the race tightening.
Many investors are weary of Rousseff's left-leaning policies, and believe either of her more centrist opponents would govern in a more business-friendly way.
Forty-nine percent of respondents said they disapproved of Rousseff's performance, compared to 40 percent who approved.
Also, 66 percent of voters said their purchasing power had declined compared to a year ago, reflecting fallout from rising inflation and an economy that has averaged just 2 percent growth since Rousseff took office in 2011.
Most political analysts still expect Rousseff to win the Oct. 5 vote, thanks to continued strong support from Brazil's poor, who have benefited from social welfare programs.
The Sensus poll was conducted nationwide between April 22 and 25, with 2,000 respondents and a margin of error of 2.2 percentage points.
© Thomson Reuters 2014
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