Match ends, Brazil 1(3), Paraguay 1(4).
Brazil 1-1 Paraguay (3-4 pens)
Paraguay repeated their 2011 Copa America penalty shootout win over Brazil to set up a semi-final meeting with Argentina.
Former Manchester City striker Robinho scored on his 99th appearance to give Brazil a 15th-minute lead as he tucked away a Dani Alves cross.
But Thiago Silva's second-half handball allowed Derlis Gonzalez to equalise from the spot and force the shootout.
Brazil then missed two attempts and went out as Gonzalez again converted.
The defeat curtailed Brazil's revival under Dunga following their 7-1 semi-final defeat by Germany in last summer's World Cup finals in their own country.
The eight-times winners have not won the Copa America since 2007, while Paraguay now have the chance to go on and lift the trophy for the first time since 1979.
They play Argentina in Concepcion at 00:30 BST on 1 July with the other semi-final seeing host country Chile meet Peru ahead of the final in Santiago on 4 July.
Brazil were unable to build on the perfect start given to them by Robinho - playing in place of the suspended Neymar - as the 31-year-old scored his first competitive goal for his country since 2010.
Robinho was helped by clever movement from Roberto Firmino, although that was virtually the only major contribution Liverpool's new £29m signing from Hoffenheim made before being replaced in the second half.
Brazil barely created another chance, while Paraguay gradually stepped up the pressure in the second half.
Defender Paulo da Silva was denied by Jefferson's save as he headed goalwards following a corner.
But an error of judgement from Paris St-Germain defender Silva gifted a deserved equaliser and Paraguay then held their nerve to progress with the tie going straight to penalties after 90 minutes.
Brazil did better than in 2011 when they failed to score a single penalty in the shootout but Paraguay could even afford a miss from former Manchester City and Blackburn striker Roque Santa Cruz as they recorded a memorable win.
- 1de Oliveira Galvao
- 2Alves da SilvaBooked at 50mins
- 14Thiago Silva
- 6Filipe Luís
- 8Mendes Trindade
- 19WillianSubstituted forDouglas Costaat 60'minutes
- 21CoutinhoBooked at 76mins
- 20de SouzaSubstituted forde Barros Ribeiroat 87'minutes
- 11FirminoSubstituted forTardelli Martinsat 69'minutes
- 4David Luiz
- 7Douglas Costa
- 9Tardelli Martins
- 12Murara Neto
- 15Cerqueira Teles
- 18de Barros Ribeiro
- 5ValdezBooked at 25mins
- 14Da Silva
- 4AguilarBooked at 38mins
- 22ArandaSubstituted forMartínezat 77'minutesBooked at 81mins
- 11BenítezSubstituted forRomeroat 84'minutes
- 9Santa Cruz
- 18ValdezSubstituted forBobadillaat 74'minutes
- 8Barrios Caceres
- Andrés Cunha
- Shots on Target
Penalty Shootout ends, Brazil 1(3), Paraguay 1(4).
Goal! Brazil 1(3), Paraguay 1(4). Derlis González (Paraguay) converts the penalty with a right footed shot to the top right corner.
Goal! Brazil 1(3), Paraguay 1(3). Philippe Coutinho (Brazil) converts the penalty with a right footed shot to the bottom left corner.
Penalty missed! Bad penalty by Roque Santa Cruz (Paraguay) right footed shot is too high. Roque Santa Cruz should be disappointed.
Penalty missed! Bad penalty by Douglas Costa (Brazil) left footed shot is too high. Douglas Costa should be disappointed.
Goal! Brazil 1(2), Paraguay 1(3). Raúl Bobadilla (Paraguay) converts the penalty with a right footed shot to the top left corner.
Goal! Brazil 1(2), Paraguay 1(2). Miranda (Brazil) converts the penalty with a right footed shot to the bottom right corner.
Goal! Brazil 1(1), Paraguay 1(2). Victor Cáceres (Paraguay) converts the penalty with a right footed shot to the high centre of the goal.
Penalty missed! Bad penalty by Everton Ribeiro (Brazil) left footed shot misses to the right. Everton Ribeiro should be disappointed.
Goal! Brazil 1(1), Paraguay 1(1). Osvaldo Martínez (Paraguay) converts the penalty with a right footed shot to the bottom left corner.
Goal! Brazil 1(1), Paraguay 1. Fernandinho (Brazil) converts the penalty with a right footed shot to the top left corner.
Penalty Shootout begins Brazil 1, Paraguay 1.
Second Half ends, Brazil 1, Paraguay 1.
Attempt missed. Óscar Romero (Paraguay) left footed shot from long range on the left is close, but misses to the left. Assisted by Victor Cáceres.
Dani Alves (Brazil) wins a free kick in the attacking half.
Foul by Raúl Bobadilla (Paraguay).
Thiago Silva (Brazil) wins a free kick in the defensive half.
Foul by Roque Santa Cruz (Paraguay).
Foul by Fernandinho (Brazil).