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.
Juan Aurich had central defender Jesus Alvarez sent off in the 85th minute and striker Luis Tejada dismissed in injury time.
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.
Libertad left back Adalberto Roman surprised Lanus when he stole in behind the defence on the right to head home a free-kick to the far post.
The Argentine side's Paraguayan striker Santiago Salcedo was sent off in the 40th minute for a second booking.
With seven minutes remaining, Lanus left-back Maximiliano Velazquez stunned Libertad goalkeeper Bernardo Medina when he lobbed him with a shot from a narrow angle when the home defence were expecting a cross.
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.
