Madrid were beaten after conceding an early goal scored by Beñat Etxebarria.
Madrid could not force their way back into the game and could be 11 points behind leaders Barcelona if the Catalans beat Levante today.
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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.