Eight-time Copa America winners Brazil were left stunned and eliminated as they failed to convert a single penalty in their shootout against Paraguay, losing it 2-0.
The Brazilians created the better chances throughout the 120 minutes, but were unable to make the breakthrough as both sides remained scoreless to send the quarter-final in La Plata to penalties.
Paraguay, meanwhile, had goalkeeper Justo Villar to thank for their clean sheet as the Estudiantes shot-stopper kept out the likes of Alexandre Pato, Robinho and Neymar on numerous occasions. Indeed the attacking trio of Brazil looked dangerous throughout the encounter, with Neymar sending two strikes barely wide of the post either side of the half-time interval.
A goal was not forthcoming, though, and both sides were forced to play out the majority of extra-time with 10-men after Lucas Leiva and Antolin Alcaraz were shown red following a touchline fracas.
Brazil were then made to pay for squandering their chances during the match as Elano, Andre Santos and Fred all blazed their penalties horribly off target, whilst Thiago Silva's spot-kick was saved by the impressive Villar.
Paraguay will face Venezuela in the semi-finals after Cesar Farias' men overcame Chile 2-1 in San Juan.
Oswaldo Vizcarrondo opened the scoring for the Venezuelans in the 34th-minute with a glancing header past goalkeeper Claudio Bravo from a free-kick.
Star Chilean striker Humberto Suazo then restored parity on 69 minutes before Gabriel Cichero gave Venezuela the lead once again 10 minutes before full-time to send Venezuela through to the Copa America final four for the first time.
The Copa America semi-finals will begin on Tuesday with Uruguay facing Peru, while Paraguay will take on Venezuela on Wednesday after many of the tournament favourites were knocked out in the quarter-final stage.