After the scores were level at 1-1 after 90 minutes, penalties were required to settle the contest and with Everton Ribeiro and Douglas Costa both missing the target it was Paraguay who triumphed 4-3 to progress to a semi-final clash with Argentina.
It was no less than Paraguay deserved after showing considerably more desire than their more illustrious opponents.
Robinho put Brazil ahead in the 15th minute when he got on the end of a low Dani Alves cross from the right, side-footing the ball past Justo Villar.
However, rather than look to build on their advantage, Brazil sat back and invited Paraguay onto them and the tactic would eventually cost them in the 72nd minute.
Skipper Thiago Silva was penalised for handball in the area when he made use of his hand while challenging for the ball in the air, and Derlis Gonzalez made no mistake from the spot, cooly slotting the ball past Jefferson in impressive fashion.
With neither side able to add to the scoring further, the match went to penalties. Ribeiro, who had been introduced with minutes remaining seemingly for the purpose of taking a penalty, was the first to err as his side-footed effort rolled to the right of the post. Costa then blasted his effort over the top to put Paraguay very much in the ascendancy.
Paraguay skipper Roque Santa Cruz had the chance to win it for his side, but his effort was way over the bar. Philippe Coutinho kept Brazil in it, but Gonzalez would make no mistake with his effort, finding the top right corner to score his second high-pressure penalty of the night.