Classy Paraguay sink Slovakia
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.
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"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 now top the group with four points after two games with Slovakia on one, alongside world champions Italy and New Zealand, who play later on Sunday.
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."
Weiss had predicted a fast-paced match at the Free State stadium, with Martino also bracing his side for some swift Slovak counter attacks.
However, there was little evidence of either for the colourful 26,643 fans who tried in vain to lift the tempo of a match reduced to walking pace at times.
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.
It was a deserved lead and one that briefly sparked Slovakia into life. They had their best spell with defender Kornel Salata heading over from a corner after a long period of possession.
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.
Paraguay began to find joy down the right and almost grabbed a second goal after good work by striker Roque Santa Cruz.
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 before sending it high past the despairing Jan Mucha.
South American teams have now won six and drawn two of the eight games they have played in South Africa so far.
Paraguay have not gone beyond the second round in seven previous World Cup campaigns but having seen off both Argentina and Brazil in an impressive qualifying run, they just might fancy their chances of breaking that duck this time around.