After an even opening 45 minutes, the Blues dominated the second half but had to wait until the 73rd minute for their breakthrough, which arrived courtesy of Marcos Alonso's low strike.
Newcastle rarely looked like threatening Chelsea's second clean sheet of the season as the hosts picked up their fifth successive win across all competitions - the best run of form in Frank Lampard's fledging managerial career.
The Magpies held their own throughout a relatively uneventful first half, offering sporadic threats on the break and largely keeping Chelsea at bay despite the hosts enjoying the lion's share of possession.
The best chances did fall to Lampard's side, though, and Willian should have done better with the first of those when he was picked out by Callum Hudson-Odoi only to get his header all wrong and steer it off target.
Martin Dubravka was forced into his first save of the contest shortly afterwards when Jorginho and Hudson-Odoi combined to tee up Mason Mount, whose shot on the turn was too close to the Newcastle keeper.
Steve Bruce's side were limited to half-chances at the other end, with Allan Saint-Maximin and Joelinton both missing the target - the first with a half-volley from 25 yards and the second with a header while stretching for the ball.
Chelsea did not look much more likely to score themselves, though, with Willian dragging an effort wide of the near post and Alonso sending a tame looping header into the arms of Dubravka.
There was further frustration for the hosts shortly before half time when Ross Barkley was forced off with a minor injury, being replaced by Mateo Kovacic, who himself had been an injury doubt heading into the match.
Lampard's side did impose a more prolonged period of control in the second half as they began to dominate possession and territory to an even greater extent, denying Newcastle any opportunity to relieve the growing pressure.
A string of corners eventually led to Chelsea coming as close as they had all game when Tammy Abraham climbed highest in the box and crashed a thunderous header against the crossbar, with Dubravka beaten.
The home side did not relent either, and Abraham came close from another corner shortly after the hour mark when he once again rose above the defence only to this time put his header over the top.
Newcastle may have begun to believe that it would be their day when another glorious chance went begging for the hosts moments later, as Hudson-Odoi's blocked shot deflected into the path of Christian Pulisic, who was thwarted by a fine one-on-one save from Dubravka.
Dubravka then denied Willian from a tight angle before the breakthrough did finally arrive for Chelsea with 17 minutes of normal time remaining.
Hudson-Odoi had been the most dangerous player throughout the 90 minutes and it was no surprise to see him involved as he collected a pass with his back to goal inside the box before laying it into the path of Alonso, who drilled a low first-time strike into the bottom corner.
A loose pass from Andy Carroll almost gifted Hudson-Odoi the chance to get his own name on the scoresheet minutes later, but his finish was tame and easy for Dubravka to gather.
Chelsea did look certain to add a second goal 10 minutes from time when Jorginho slid the ball through for Pulisic, who found himself in a two-on-one scenario with Abraham and the keeper. Pulisic duly slid the ball to Abraham, who appeared to have a simple tap-in until DeAndre Yedlin produced a stunning last-ditch block to deny a certain goal.
The visitors never really looked capable of making that goal-saving interception truly count, though, with their only half-chance in the closing stages seeing Ciaran Clark steer the ball off target with a difficult header.
The result lifts Chelsea up to third in the table for a few hours at least, whereas Newcastle have now slipped into the relegation zone courtesy of Southampton's draw at Wolverhampton Wanderers.
CHELSEA (4-3-3): Kepa; Azpilicueta, Zouma, Tomori, Alonso; Barkley (Kovacic 43'), Jorginho, Mount (Pulisic 64'); Willian, Abraham, Hudson-Odoi (James 92')
NEWCASTLE (5-4-1): Dubravka; Yedlin, Schar, Lascelles, Clark, Willems; Almiron (Carroll 70'), M Longstaff, S Longstaff, Saint-Maximin (Gayle 85'); Joelinton (Atsu 83')