Paraguay goalkeeper Justo Villar stopped Thiago Silva’s shot and Elano, Andre Santos and Fred also missed for Brazil, which was eliminated from the South American competition a day after host Argentina lost to Uruguay.
Paraguay will face either Chile or Venezuela, which will play later Sunday. Uruguay and Peru, which eliminated Colombia on Saturday, will meet in the other semifinal.
Brazil was trying to win its third straight Copa America title having won four of the past five tournaments. Coach Mano Menezes brought a mixed squad of veterans and promising young stars in preparation for the 2014 World Cup at home.
Paraguay advanced despite not winning any of its four matches so far.
Marcelo Estigarribia and Christian Riveros scored for Paraguay in the shootout after Villar capped his great performance by diving to his left to stop Thiago Silva’s shot.
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