Mauricio Pellegrino's men needed goals from Ezequiel Cerutti and Diego Vera in the final 14 minutes to edge to the win at the Estadio San Juan del Bicentenario.
The win saw Estudiantes into the last eight, where they will face Argentinos Juniors.
Just nine minutes later, Cerutti was unlucky not to have a second – but his missed effort did lead to the sealer.
The substitute's 35-yard free-kick crashed off the crossbar before hitting the goal-line, and Vera was on hand to nod in the easiest of goals to send Estudiantes through.
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