It was a fourth successive defeat for ailing giants Racing, who had begun the season with promise by notching up two wins with a team brimming with talented new signings including Colombia's Giovanni Moreno.
Racing fans lost their patience and called for coach Miguel Angel Russo to quit. He told reporters: "We can turn this round."
The top two have 13 points after Velez were held 0-0 at home by San Lorenzo, who are a point further back.
Estudiantes bounced back from the disappointment of losing the South American Supercup final to LDU Quito of Ecuador in midweek.
Winger Enzo Perez put Estudiantes ahead one minute into the second half with a low shot from the edge of the box across keeper Jorge De Oliveira and into the bottom far corner.
Former Racing defender Gabriel Mercado added the second in the 55th minute as Estudiantes took charge and the visitors, who were on top in the first 30 minutes but missed their chances, lost their way.
Estudiantes have a match in hand over Velez, the La Plata "clasico" against Gimnasia.
Gimnasia, who were beaten 2-0 at Tigre on Friday, have yet to score in five matches and are one of four teams with two points.
