Leo Messi scored a sublime free kick to wrap up the win and leave Paraguay in real danger of missing out on qualification.
Ecuador beat Bolivia 1-0 to move second in qualifying, whilst Uruguay were stunned by a 4-0 defeat to Colombia.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.