Substitutes Pablo Aguilar and Oribe Peralta scored three times in the final 12 minutes to effectively send America into the semi-finals, with Deportivo Saprissa needing to win by at least three goals in Mexico to overhaul their opponents.
America only had four shots on target to Saprissa's eight but ripped the home side's defence apart late in the match.
Aguilar headed Rubens Sambueza's cross inside the back post in the 78th minute, while three minutes later, Peralta converted from Carlos Quintero's cutback.
Peralta wrapped up America's triumph in the 84th minute, toe-poking past Saprissa goalkeeper Danny Carvajal after a chip over the top from Aguilar.
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