Newcastle United have now lost six consecutive games at Stamford Bridge in all competitions, conceding 18 goals while scoring just twice themselves as Michy Batshuayi scored twice to see 2017 finalists reach the fifth round of the FA Cup.
Batshuayi rounded off a superb move to open the scoring before putting the finishing touch to another Chelsea attack just before half-time.
He is the third Chelsea player to reach double figures for goals in all competitions this season for Chelsea after Alvaro Morata and Eden Hazard (12 each).
Marcos Alonso’s second-half free-kick sealed the win for the home side.
Antonio Conte has been linked with a string of strikers, including Edin Dzeko, Andy Carroll and Ashley Barnes, in a bid to add back-up for Alvaro Morata, but on this evidence the answer may lie closer to home.
Batshuayi recorded his 10th goal of the season in all competitions shortly before the break, Jamaal Lascelles’ attempted block from the Belgian’s shot looping the ball over goalkeeper Karl Darlow and in.
Alonso’s sublime 25-yard free-kick wrapped up the victory and Chelsea’s unbeaten run at home stretches to 15 matches, while Newcastle’s appalling FA Cup record continues, with the Magpies last reaching the fifth round in 2006.