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It didn't start well for the Premier League champions though as Dwight Gayle gave the Magpies the lead in the 12th minute following a defensive mix up.
The Blues were only behind for nine minutes though as Hazard scored the first of his two at Stamford Bridge.
Morata put Chelsea ahead with an eady header following an inch perfect cross from Victor Moses in the 33rd minute to turn the game around.
Newcastle stayed in the game until 15 minutes from the end when Antonio Conte's side were awarded a penalty.
Hazard stepped up confidently and have Karl Darlow no chance in goal.
The result leaves Chelsea in third, level on points with Manchester United before they take on Arsenal later today.
Chelsea player ratings v Newcastle

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