The long-time Primera Division club, now in the second tier of Argentine football, were awarded two penalties against third-tier Santamarina.
Federico Insua slotted Independiente's first spot-kick, while Cristian Menendez converted the second, as the home side triumphed comfortably.
Santamarina scored the last goal of the match, which gave the visitors some momentum in the closing stages.
Insua, formerly of Velez Sarsfield, Boca Juniors, Borussia Monchengladbach and Malaga, put Independiente in front from 11 metres in the 26th minute.
Fabian Monserrat doubled the hosts' lead in the 35th minute before Ignacio Celaya dragged Santamarina back into the contest four minutes before half-time.
Insua completed his brace just after the hour-mark before Menendez made it 4-1 from the spot in the 65th minute and, although the visitors scored again through Maximiliano Timpanaro with 19 minutes left, Independiente advanced.
The Avellaneda-based club were joined in the round of 32 by Ferro Carril Oeste, who defeated Atletico Tucuman 1-0.
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