Kevin Gameiro got the only goal of the game for Carlo Ancelotti’s side.
That moves them level on points with Marseille and ahead on goal difference, although their rivals have a game in hand on Sunday.
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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.