Man-of-the-match Jose Sosa brilliantly beat three men at close quarters in the box and squared the ball for striker Gaston Fernandez to open the scoring in the 51st minute.
Midfielder Rodrigo Brana then superbly beat goalkeeper Diego Morales with a lob from the centre circle in the 67th minute to make the result safe.
Estudiantes took the first half to get used to the synthetic Elias Aguirre pitch in Chiclayo and control the home side's speedy forwards before imposing their well organised game.
The Argentine side have taken 10 points from five matches. They are two ahead of Peru's Alianza, who can reclaim the lead if they beat eliminated Bolivar of Bolivia at home next week. Juan Aurich have six points and Bolivar one.
In Group Four, 10-man Lanus of Argentina snatched a 1-1 draw away to Paraguay's Libertad in a poor match at the Defensores del Chaco stadium in Asuncion.
The Argentine side's Paraguayan striker Santiago Salcedo was sent off in the 40th minute for a second booking.
The group is led by Libertad with nine points from five matches. Peru's Universitario are second with eight points and a match in hand. Lanus have seven points while Bolivia's Blooming have none.
