Antolin Alcaraz opened the scoring when he beat his marker in the air to head home an Aureliano Torres curling long free kick six minutes from the interval.
From point-blank range, Italy's Daniele De Rossi volleyed a corner kick into the net after keeper Justo Villar overshot the ball while trying to punish it away.
The match was by far eventless, with both sides barely able to create scoring chances.
Italy goalie Gianluigi Buffon made way for Federico Marchetti right after the break.
It was reported that the towering keeper was taken off because his back problem resurfaced after the first half.
The full extent of his injury is yet to be determined.
Italy got the upper hand midway through the second half but couldn't snatch a victory over the South American side.