Both goals came from Arturo Vidal, the Chilean firing the Bianconeri to a crucial win.
The champions are now 11 points clear of second place Napoli, and are on course to retain their title.
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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.