Blackburn Rovers Roque Santa Cruz paved the way for the defeat of the five-time world champions with a goal in the first half, followed by another by Salvador Cabanas in the second half.
Paraguay went down to 10 men two minutes after the break when right back Dario Veron was handed a second yellow card for a tackle from behind, earning his dismissal.
Brazil coach Dunga, surely with one eye on Wednesday's home clash with Argentina in Belo Horizonte, must have rued the absence of attacking flair of AC Milan’s Kaka, who recently had knee surgery and became a father for the first time, and out-of-form Barcelona striker Ronaldinho.
Early on Robinho broke through into Argentina's box but the move came to nothing, moments before Cabanas gained possession on the edge of the area and hit the right hand post of well-beaten Brazilian keeper Julio Cesar.
Brazil showed defensive frailty when Paraguay went ahead in the 26th minute.
A slightly mis-hit corner by Edgar Barreto, who had an excellent match, caused confusion at the near post and the ball shot through a crowded six-yard box for recent Blackburn recruit Santa Cruz to sidefoot home at the far post.
Luis Fabiano bustled into the box and fed Robinho but he just could not make contact with the ball as he slid into Paraguay keeper Justo Villar.
Paraguay however started to dominated just before the break and were continually trying to break through their opponents’ back line.
Barreto had a dangerous-looking free kick on the right hand side of the box but the team of Argentinian coach Gerardo Martino could not make it count.
Argentina substitute Rodrigo Palacio scored in the fourth minute of stoppage time, five minutes after coming on, to salvage a 1-1 home draw against Ecuador in their World Cup qualifier.
Ecuador had been poised to hand Argentina their first home defeat in a qualifier since 1993 after going ahead with a brilliant strike from Patricio Urrutia in the 69th minute.
The draw left Argentina with 10 points from five games in the South American group, and Ecuador with four.
The visitors surrounded referee Rene Ortube at the end, apparently angry at the amount of time he had added on. Argentina, who visit arch-rivals Brazil in another qualifier on Wednesday, were generally unimpressive.
A poor first half failed to produce any clear cut chances. With Juan Roman Riquelme having a quiet game in midfield, Argentina failed to get the ball to strikers Lionel Messi and Sergio Aguero.
Their best move ended with Messi just failing to make contact with a low cross from Maxi Rodriguez.
Riquelme wasted two free kicks early in the second half before Ecuador had a penalty appeal turned down when Joffre Guerron burst into the area and appeared to be pushed over by Gabriel Heinze.
Guerron and Carlos Tenorio were a constant problem for the Argentine defence and both were involved in the a superbly-worked goal in the 69th minute. The pair combined for Tenorio to backheel the ball into the path of Urrutia, who rifled in a 20-metre shot off the crossbar.
Argentina replied with a Julio Cruz header which flew just wide before Aguero forced a good save from goalkeeper Jose Cevallos.