Timo Werner scored his first goal in 15 Premier League matches as Chelsea moved up to fourth in the table.
Werner set up Olivier Giroud for the opening goal just after the half-hour mark and doubled the lead six minutes before the interval.
The Blues remain unbeaten under boss Thomas Tuchel – who sprang a surprise by selecting the much maligned Kepa rather than Edouard Mendy in goal.
Giroud came on as a substitute for Tammy Abraham, who limped off after 20 minutes with what seemed like a nasty ankle injury.
Abraham was hurt by a challenge from Jamaal Lascelles, whose last-ditch tackle thwarted the striker after he found himself in on goal.
Otherwise it was a very positive night for Chelsea – and for third-from-bottom Fulham, who are a place below Newcastle in the table and trail them by seven points after winning at Everton on Sunday.
Chelsea went ahead when Werner did superbly on the left and the German’s low cross was parried by keeper Karl Darlow towards Giroud, who netted from close range.
And Werner ended his barren run when Newcastle failed to deal with Mason Mount’s right-wing corner.
After a ricochet after Lascelles, the German was able to scoop the ball over the line before Darlow could get to it.
Chelsea: Kepa, Azpilicueta, Christensen, Rudiger, Hudson-Odoi (James 77), Jorginho, Kovacic, Alonso, Werner, Mount (Kante 70), Abraham (Giroud 45).
Subs not used: Mendy, Pulisic, Zouma, Chilwell, Ziyech, Emerson.