Robinho had given the Selecao the advantage after just 14 minutes, but Dunga’s side surrendered their lead with 18 minutes of normal time remaining as Derlis Gonzalez stepped up to convert a spot-kick to send the tie to a shoot-out.
Fernandinho completed the full game - and netted his penalty - but could do nothing to prevent his side from exiting the tournament and suffering a repeat of the events of the 2011 competition. Paraguay emerged victorious in that quarter-final encounter on penalties too.
The result means Ferna will miss the chance to lock horns with Sergio Aguero, Martin Demichelis and Pablo Zabaleta in the last four.
As La Albiceleste had already booked their place in the semis, Brazil had known what lay ahead before their last eight game but a poor second half showing cost them.
A Paraguay fightback had looked unlikely after Robinho opened the scoring. Even before then, Philippe Coutinho had already forced Justo Villar into a save with a long-range attempt.
The deadlock was broken when a well-worked Brazilian move saw Elias feed Dani Alves out wide. The right-back curled in a low first-time cross to the ex-City star at the backpost, who tapped home from close range.
Despite responding with a period of possession, Paraguay were unable to really trouble Jefferson.
Former Blue Roque Santa Cruz’s low drive was the closest La Albirroja came to finding an equaliser in the first 45 minutes, but it was well wide of the target.
After the break though, they were much more threatening.
Gonzalez’s whipped free-kick did call the Brazilian shot-stopper into action at his near post, before Nelson Valdez headed over from a corner.
Another set-piece caused havoc moments later as Jefferson did well to block Paulo da Silva’s header and as the onslaught continued, they earned their reward when referee Andres Cunhar awarded a penalty for handball against Thiago Silva.
Up stepped Gonzalez to despatch it expertly and level the score.
He almost netted a second with ten minutes of normal time remaining but fired his shot straight at Jefferson as Paraguay instigated another dangerous counter-attack.
At the other end, Coutinho’s effort almost caught Villar out and Alvez curled a free-kick wide.
In the last action of the 90, Oscar Romero went for glory with seconds remaining only to scuff wide and the clash was sent to penalties.
Fernandinho was the first to step up, smashing a powerful effort through the goalkeeper, who did make contact but could not block the shot.
It was the perfect start for the Brazilians but it would all go downhill from there. Everton Ribeiro skewed his effort wide while Osvaldo Martinez and Juilo Caceres converted theirs.
Miranda did score his - as did Raul Bobadilla for Paraguay - before Douglas Costa blazed over, meaning one more successful Paraguayan penalty would secure victory.
Santa Cruz missed the chance to clinch it - but it did not prove detrimental. Although Coutinho found the net, Gonzalez did too to break Brazilian hearts and set up a semi-final clash with Argentina on Tuesday 30 June at 00:30 BST.
