Second placed Atletico went ahead through Radamel Falcao but Adriano equalised before Sergio Busquets put them ahead.
Two goals from Leo Messi wrapped up the win and ensured Barcelona remain clear at the top.
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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.