In a potential runoff, Lula would receive 46% of voter support, compared with 44% for the eldest son of former President Jair Bolsonaro, the poll said, Reuters reported.
Lula's narrow runoff lead remains within the survey's margin of error.
A September 21 survey had Lula leading Bolsonaro by 46% to 45%.
In a first-round scenario, Lula would lead with 42% of the votes, followed by Bolsonaro (37%), Augusto Cury (5%), Ronaldo Caiado (5%) and Renan Santos (4%).The previous first-round survey had Lula at 40% and Bolsonaro at 37%.
If no candidate wins more than 50% of valid votes in the October 4 first round, the two frontrunners will advance to a runoff on October 25.
Nexus surveyed 2,000 people from September 25 to 27. The poll has a margin of error of 2 percentage points.