Marcos Alonso’s second-half strike broke Newcastle’s resistance as Chelsea moved up to third in the Premier League with their fifth successive win in all competitions.
The Blues seemed set for another frustrating day at Stamford Bridge after Tammy Abraham saw his header hit the bar and Martin Dubravka denied Christian Pulisic.
But they finally got their reward for relentless second-half pressure when Spanish left-back Alonso drove in a firm, angled shot in the 73rd minute.
They should have scored a second through Abraham, but the England international’s shot was brilliantly blocked by DeAndre Yedlin.
Steve Bruce’s Magpies were preoccupied with defending for much of the match and failed to test Kepa Arrizabalaga.
Defeat means they drop into the relegation zone, although their manager will point to the fact they have now played every one of the ‘big six’ in their first nine games, bar Manchester City.