Well-taken goals from Enrique Vera and Cristian Riveros in the 27th and 86th minutes were too much for a toothless Slovakia side who posed no threat to the South Americans.
"We were good in defence, we did well in attack. It was a great match. We scored and we feel close to the round of 16," man-of-the-match Vera told reporters.
Paraguay coach Gerardo Martino added: "I think these results have strengthened us mentally, spiritually, not just as football players, especially in our attitude. We are getting closer to our objectives to make it to the final rounds."
Slovakia's first World Cup appearance is likely on borrowed time, with Italy still to come on Thursday, while Paraguay will expect to beat New Zealand the same day to progress.
"We made two mistakes. It was a high quality opponent and their victory was deserved," Slovakia coach Vladimir Weiss conceded to reporters after the game.
"We lost the match because we were not bold upfield. Paraguay didn't play as good as they can and still we lost."
The first half was lit up only by Vera's superb finish.
Paraguay's three-pronged attack had found space on the edge of the box and began to put it to good use when Lucas Barrios's delicate pass was met by the outside of Vera's right boot as he dispatched a curling effort into the net from 12 metres.
In the second half, the game slowed down even more with Slovakia's statistic of one shot on target telling the story of lone striker Robert Vittek's fruitless afternoon.
But they did eventually stretch their lead four minutes from time thanks to Riveros's sweet left foot.
The midfielder, who joined English Premier League side Sunderland from Mexico's Cruz Azul on a free transfer last month, collected Paulo Da Silva's square ball on the edge of the box b
