First-half goals from Olivier Giroud and Timo Werner gave the Blues all three points as the Magpies remained 17th in the Premier League table, seven points ahead of Fulham below them.
Our Newcastle United writer Miles Starforth has dished out his player ratings from the match – scroll down and flick through the pages of our picture gallery to see if you agree:
1. Karl Darlow - 6
Left exposed for Chelsea's first-half goals, had a quieter second half thanks to an improved performance. 6 Photo: Gareth Copley
2. Emil Krafth - 4
Had a nervy start against Werner and the over-lapping Alonso, and Chelsea got their breakthrough from an attack down United’s right side, needed more help. 4 Photo: Getty Images
3. Jamaal Lascelles - 6
Denied Abraham with a goal-saving challenge early in the game. 6 Photo: Pool
4. Ciaran Clark - 6
Restored to the team after missing the Southampton game to be with his partner when he went into labour, put in a committed performance, tried to turn defence into attack. 6 Photo: Stu Forster