Kai Havertz's superb late strike condemned Newcastle to a first defeat in 10 matches as Chelsea secured a hard-fought victory at Stamford Bridge.
Chelsea started brightly, with Andreas Christensen sending an effort narrowly over on two minutes before Mason Mount's curling free-kick tickled the side-netting.
Newcastle dug in and created chances of their own as Dan Burn headed wide from Miguel Almiron's cross on 34 minutes before the latter's crisp 25-yard volley was pushed away at full stretch by Edouard Mendy on the stroke of half-time.
The visitors continued to frustrate Chelsea after the break and Havertz headed straight at Martin Dubravka moments before Matty Longstaff's dipping effort flew over.
Havertz finally made the breakthrough on 89 minutes, picking up Jorginho's brilliant ball over the top and slotting in from close range
Chelsea stay third on 59 points, 11 off leaders Manchester City and eight clear of Arsenal in fourth. Newcastle remain 14th on 31 points.
Chelsea: 2 Apr v Brentford (H)
Newcastle: 17 Mar v Everton (A)
Referee: David Coote. Assistants: Ian Hussin, Nick Hopton. Fourth official: Michael Sailsbury. VAR: John Brooks. Assistant VAR: Sian Massey-Ellis.