Elano, Thiago Silva, Andre Santos and Fred all failed to convert from 12 yards while Estigarribia and Estigarribia scored to send Paraguay into the semi-final.
Meanwhile on Saturday night Uruguay dumped out Argentina, with Carlos Tevez’s penalty miss proving crucial in the quarter-final shootout.
Gonzalo Higuain’s equaliser had got Sergio Batista’s side level in the 17th minute, cancelling out Diego Perez’s early opener, and things looked to have turned in the hosts’ favour when Perez was sent off on 39 minutes.
But Javier Mascherano’s red card evened up the numbers and, when there were no further goals after extra time, Fernando Muslera took centre stage. He made the only save of the shootout from Tevez’s effort.