Midfielder Cesar Gonzalez scored the goal that stunned Ecuador and put Venezuela two points clear of Brazil and Paraguay with one match to go in their group.
Brazil, for whom playmaker Paulo Henrique Ganso laid on both goals with similar defence-splitting passes, took the lead six minutes before half-time at the Mario Alberto Kempes stadium in Cordoba.
Midfielder Ramires gained possession at the breakdown of a Paraguay attack and fed Ganso, who touched the ball perfectly through to Jadson and he wasted no time shooting from the edge of the area low into the bottom corner.
Roque Santa Cruz equalised 11 minutes after the interval when the Brazilian defence failed to clear Marcelo Estigarribia's cross from the left into the middle of the box and the striker shot into the bottom corner past Julio Cesar.
Paraguay went ahead 12 minutes later when the ever-dangerous Estigarribia robbed Daniel Alves on the left of the area and squared to the middle where substitute Nelson Haedo Valdez's shot came off Lucio but he put it away at the second attempt.
Brazil snatched the equaliser when striker Fred took a perfect through pass into the box from Ganso and fired low past goalkeeper Justo Villar.
Paraguay coach Gerardo Martino, rather than ruing Brazil's late equaliser, said he was pleased with the progress shown by his team in a tight tournament since they reached the last eight at the 2010 World Cup.
"Beyond the result, I can say that after two matches here, we have played better than in the World Cup and we have fewer points," Argentine Martino told the post-match news conference.
The goal by midfielder Jadson, replacing Robinho in the only change to Brazil's side from the 0-0 draw with Venezuela in La Plata last Sunday, was the first in the group after the opening two matches had finished scoreless.
Brazil coach Mano Menezes, regretting their defensive mistakes, said: "It would have been unfair to have come away from this match defeated. Paraguay did little to beat us.
"We had two other good chances that we missed through making the wrong choice [at the finish]... the final round of [group] games has become decisive because of what [the four teams] have done up to now."
At the Padre Ernesto Martearena stadium in Salta, Venezuela footballers took another big step in shaking off their tag as a baseball nation, by deservedly beating Ecuador for only their third ever win in the competition.
"Maestrico" (Little Master) Gonzalez scored the only goal just past the hour when he fired in a shot from outside the box past static goalkeeper Marcelo Elizaga, who was unsighted by one of his defenders.
Ecuador, without Manchester United winger Antonio Valencia, who is nursing an ankle injury, squandered several chances to save the game with hurried efforts to score an equaliser.
The group placings will be settled on Wednesday when Paraguay meet Venezuela in Salta and Brazil face
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