Brazil – desperate to bounce back after a demoralising 2-2 draw with Uruguay on Friday when they squandered a two-goal lead – appeared to be heading to defeat after Dario Lezcano and Edgar Benitez put Paraguay 2-0 up.
But Ricardo Oliveira gave Brazil hope with a right-footed strike to make it 2-1 on 79 minutes and, sensing opportunity, the visitors swarmed forward in search of an equaliser.
Two minutes into stoppage time, Chelsea forward Willian advanced down the right flank and fed Alves, who darted into the penalty area purposefully.
Paraguay’s defence stood off fatally and the Brazilian fullback curled his shot beyond the fingertips of veteran goalkeeper Justo Villar.
Brazil might even have snatched a remarkable victory after the late equaliser.
Once again Alves was involved, thumping a dipping shot goalwards which Villar could only parry away.
Filipe Luis followed up but was just unable to direct the ball into the net for Brazil in a nerve-jangling scramble inside the six-yard box with just seconds left.
Brazil now stands in sixth place in the standings with nine points from six games, just behind fifth-placed Colombia and fourth place Chile, who have 10 points.
Argentina are in third place with 11 points, two behind leaders Uruguay and Ecuador.
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