Paraguay returned to haunt Brazil once more at the Copa America, knocking out Dunga's side on penalties 4-3 in their quarter-final in Concepcion on Saturday.
After failing to score from the spot in their 2-0 shootout loss to the Paraguayans at the same stage four years ago, Brazil once again fluffed their lines when it mattered - with Everton Ribeiro and Douglas Costa crucially missing.
Robinho put Brazil ahead after 15 minutes, but Derlis Gonzalez's penalty midway through the second half ensured normal time finished 1-1.
Justo Villar stood in Paraguay's goal as he did four years ago in Argentina, and Ribeiro and Douglas Costa both missed the target with the custodian not required to keep them out.
Roque Santa Cruz could have sealed it with Paraguay's fourth kick, but he missed - however, Gonzalez buried his second penalty of the day to send them through to a semi-final against Argentina.
The fixture marked Brazil's first knockout match of any kind since their 7-1 drubbing at the hands of Germany at the World Cup.
Paraguay's good record against Brazil at the event continued, remaining unbeaten in their past four Copa clashes.
Both sides deployed 4-2-2-2 formations from the outset, but that was where the selection similarities ended - with Ramon Diaz making five changes to the side that drew 1-1 with Uruguay, while Brazil remained unchanged after their 2-1 win over Venezuela.
Victor Caceres, Pablo Aguilar, Eduardo Aranda, Santa Cruz and Gonzalez came in for Paraguay.
Brazil, meanwhile, looked efficient in attack in their second straight Neymar-less game.
It took less than two minutes for Dunga's men to register a shot on target - Philippe Coutinho's effort from range forcing goalkeeper Villar to tip the ball over his crossbar.
Edgar Benitez was proving to be a thorn in Brazil's side down Paraguay's left flank early on, but it was the Brazilians who took the lead in the 15th minute.
In the middle of the park, Elias - who had received the ball from Robinho - played a pass wide right for Dani Alves, whose probing cross eventually fell back to an unmarked Robinho, who had a straightforward tap-in.
Coutinho was giving Paraguay all sorts of problems on the left wing, but he almost produced a magical moment just prior to the half-hour mark on the right byline.
With Bruno Valdez trying to shepherd the ball out for a goal-kick, Coutinho somehow kept it in and played a ball back across goal - only for the sideline referee to adjudge the ball had crossed the line.
Paraguay had their moments leading up to half-time, Santa Cruz trying his luck from range and a Benitez corner causing the Brazil defence problems.
Benitez continued to push Brazil on the left side, with Dani Alves yellow-carded for a foul on him five minutes after the interval.
Paraguay's push to get back into the match saw Paulo da Silva power an on-target header at Brazil goalkeeper Jefferson, who parried it clear in the 62nd minute - but Diaz's men were level with 18 minutes to play via Gonzalez.
Both goalkeepers were called upon in the final stages - Gonzalez firing an acute-angle strike at Jefferson, before Coutinho's dipping shot made Villar work.
But neither side could create a decisive second goal, as a shootout ensued - and Brazil suffered penalty heartbreak again.
