After last week's goalless draw, Estudiantes returned home and edged Argentine rivals Gimnasia La Plata 1-0 at the Estadio Ciudad de La Plata.
Diego Vera's 50th-minute strike was all that separated the two sides over two legs.
The Uruguayan forward got on the end of Mauricio Rosales' cross and headed past Gimnasia goalkeeper Fernando Monetti.
Visitors Gimnasia ended the match with 10 men following Lucas Licht's second yellow card in injury time.
Meanwhile, Deportivo Cali are in the box seat heading into the second leg after earning a 2-2 draw at Penarol.
Uruguayan hosts Penarol took the lead three minutes into the second half courtesy of Carlos Nunez, who fired low past Luis Hurtado, before Sergio Herrera levelled proceedings six minutes later.
Cali were all-square for just four minutes after Marcelo Zalayeta restored Penarol's lead with a powerful header but Carlos Rivas' thunderous 69th-minute strike ensured the visitors returned to Colombia poised to advance.
Caracas also played out a draw away from home in the first leg of their second-round fixture, Romulo Otero's 90th-minute goal cancelling out Cristian Lopez's opener.
Paraguay's Deportivo Capiata hit the front through Lopez three minutes before half-time and were on track for victory, only for Otero to net a priceless away goal for the Venezuelans.
Independiente del Valle were the only team to win their opening leg on Wednesday after accounting for Paraguayan outfit Cerro Porteno 1-0 in Ecuador.
Arturo Mina's 56th-minute goal was enough for Independiente to claim the victory.