The result means they are six points adrift of Juventus, who they face on Friday night at the San Paolo.
More concerning still could be the form of Edinson Cavani, who has not scored in four games now.
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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.