Enrique Vera scored first for the South Americans in the 27th minute. Receiving a pass from Lucas Barrios from the left side, Vera sent the ball into the net from a distance 12 metres.
The goal put the Slovaks on high alert, who stepped up the already-tough defence further. The next set of attacks were blocked by Kornel Salata and goal-keeper Jan Mucha. Muncha made a brilliant save of the Roque Santa Cruz's shot.
Even though Paraguay had to enter the field for the second half without the striker Robert Vittek, the team managed to secure a second goal from Cristian Riveros in 86th minute.
With the Sunday, Jun 20 victory against Slovakia, the South Americans have emerged on top of the Group F. Paraguay has pocketed four points, while Slovakia has just one.
In another Group F tie-up on the same day, Italy and New Zealand, with one point each, gathered another point each by pulling off a draw in Nelspruit.