Her main challenger, Aecio Neves, has the backing of 22 percent of potential voters while Eduardo Campos has 8 percent, according to the survey broadcast on TV Globo.
In a second-round runoff vote, Rousseff would defeat Neves with 41 percent of the vote compared with his 33 percent, the survey found.
Two other polls in the past week have predicted a statistical tie.
The IBOPE poll surveyed 2,002 people from July 18-21 and has a margin of error of 2 percentage points.