Newcastle made a confident start but Chelsea created the first threat after six minutes when Danny Drinkwater's cutback was scrambled away.
The visitors' Mikel Merino sent a tame curling effort straight at Thibaut Courtois four minutes later amid some uncertain home defending.
And Newcastle profited from more uncertainty after 12 minutes as a long ball over the top enabled Jacob Murphy to threaten and, when Courtois thwarted him, Dwight Gayle slid the ball home from close range.
That woke the champions up and, after Andreas Christensen had hit a post, they were level with 21 minutes gone when Eden Hazard got onto the end of a dropping ball and sent his finish into the ground and over Newcastle keeper Karl Darlow.
Shortly after the half-hour, resurgent Chelsea were in front as Victor Moses fizzed in a cross and Alvaro Morata thumped the header past Darlow.
Newcastle were under increasing pressure but, with half-time looming, almost conjured an unlikely equaliser when Florian Lejeune's volley cannoned off Marcos Alonso and wide.
Moses was involved again early in the second half when his low cross from the right was scrambled away from Morata, and then Hazard stumbled at the crucial moment after a fine long pass by Cesc Fabregas had been headed down by Morata.
As Newcastle tried to respond, Ayoze Perez fired wide from 25 yards, but Chelsea were dominant and almost added a third with 20 minutes to go when a lovely touch from Drinkwater gave Hazard a chance he was unable to take.
But the Belgium international was on the mark again when he dinked home a penalty given for Matt Ritchie's 74th-minute foul on Moses and almost completed a hat trick when Darlow denied him after another Morata assist.
Tiemoue Bakayoko and Willian came on for the outstanding Hazard and Fabregas as the game entered its closing stages, with Christensen making way for Gary Cahill soon afterwards as Chelsea cruised to three more points.
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