The first opening - of sorts - fell to the hosts after a nice cross to the far post from Alejandro Garnacho, but Chelsea academy graduate Lewis Hall was able to poke it away before the in-form Joao Pedro could poach another goal.
The resulting corner was turned behind once more, and Wesley Fofana came close at the second time of asking, heading narrowly over the bar from the set-piece.
The Blues continued to pile on the pressure, with both Garnacho and Cole Palmer spurning presentable opportunities inside 15 minutes.
But the breakthrough came against the run of play, when Joe Willock capitalised on a ragged defensive line to run clear of the Chelsea defence, squaring to Anthony Gordon for a tap-in.
Fofana did not cover himself in glory, and was in trouble again a little later, surviving a brief red card check after felling Gordon as he looked to run through on goal.
VAR again favoured the hosts towards the end of the half, declining to send Paul Tierney to the monitor after Reece James appeared to haul down Malick Thiaw in the box from the now-standard corner-kick melee.
Liam Rosenior introduced Liam Delap at half-time, and he almost had an immediate impact, forcing a smart save out of Aaron Ramsdale.
But the match quickly settled into a familiar rhythm, with the visitors looking largely unperturbed at the back and threatening on the break.
A misjudged pass from Robert Sanchez nearly spelt disaster for the home side, but Fofana somewhat made up for his earlier error with a strong challenge on Gordon.
The VAR pendulum swung the Magpies’ way when Nick Woltemade seemingly felled Palmer in the box, the makeshift midfielder never looking especially comfortable in his role.
The strong appeals were waved away, and though Chelsea kept knocking, they simply could not find a route to goal.
Delap came close to an equaliser five minutes from time with a glancing header that drifted wide, before a stoppage-time James free-kick glanced off the post, but the visitors hung on for the win.
Chelsea have now won just two of eight home league games this season against teams who started the round in the bottom half of the table.
They therefore miss out on the chance to pull level on points with Aston Villa and Manchester United above them, while Eddie Howe’s side rise to ninth and within six points of their hosts.
Flashscore Man of the Match: Anthony Gordon (Newcastle)
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