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:
9. Miguel Almiron - 5
Perked up in the second half, covered a lot of ground, as usual, but struggled to create opportunities in the final third of the pitch. 5 Photo: JAN KRUGER
10. Allan Saint-Maximin - 5
Didn’t get into his stride before being taken off with 20 minutes left, well-marked by Chelsea. 5 Photo: Gareth Copley
11. Dwight Gayle - 4
His main contribution was a defensive header which denied Azpilicueta, otherwise had a very quiet game up front. 4 Photo: Getty Images
12. Joelinton - 5
(for Gayle, 64) Took up Gayle's position on the right side of United's attack. 5 Photo: Pool