Nicolas Jackson gave the hosts the lead in the 18th minute after Cole Palmer sliced through Eddie Howe's side with a perfectly weighted pass for Pedro Neto, who sprinted past Fabian Schar before he squared across goal to an unmarked Jackson.
Alexander Isak equalised in the 32nd minute when he tapped home from close range after Harvey Barnes worked the ball to Lewis Hall on the left of Chelsea's box before Hall crossed towards Isak, but Palmer's strike from the left of the box into the bottom-left corner shortly after half time restored the Blues' lead.
The result means that the Blues are in fourth place with 17 points after nine league games and are now above fifth-placed Arsenal, though the Gunners could leapfrog them should they pick up a point against Liverpool on Sunday.
As for the Magpies, they are 12th in the table with 12 points and have failed to win any of their last five matches in the Premier League, losing three times and drawing twice.
Palmer thought he had given Chelsea the lead in the fourth minute when Jackson played him through on goal, but he was adjudged to have been offside.
The Englishman proved vital for the Blues when he picked up the ball and split Newcastle's defence with an exceptional pass in the 18th minute for Neto, and Jackson continued his fine form in front of goal, scoring his 10th Premier League goal in his last 14 games.
Chelsea will question why their defence allowed Isak so much freedom to drift into the box for the Magpies' equaliser, and Newcastle will no doubt question why Palmer was allowed to carry the ball from the halfway line unopposed, while Nick Pope will be disappointed that he allowed Palmer's strike to sneak in at his near post.
CHELSEA VS. NEWCASTLE UNITED HIGHLIGHTS
Nicolas Jackson goal vs. Newcastle United (18th min, Chelsea 1-0 Newcastle United)
Cole Palmer slices through Newcastle's defence with a pass in behind their backline from deep in his own half to a sprinting Pedro Neto, who squares across the box to Nicolas Jackson before the striker sweeps the ball into the back of the net. What a pass from Palmer!
Alexander Isak goal vs. Chelsea (32nd min, Chelsea 1-1 Newcastle United)
Harvey Barnes works the ball to Lewis Hall, who powers a cross into the box towards Alexander Isak and the unmarked forward taps home from close range. Where was Chelsea's defence?
Cole Palmer goal vs. Newcastle United (47th min, Chelsea 2-1 Newcastle United)
Romeo Lavia wins possession in midfield and pokes the ball to Palmer, who carries the ball virtually unopposed into the box and unleashes a shot towards the left of the net which Nick Pope will feel he could have done more to save. Chelsea are back in front!
MAN OF THE MATCH - COLE PALMER
Palmer ran the show against Newcastle, as he has done so throughout the season for Chelsea, and he is unfortunate to not have scored earlier than he did given his strike in the fourth minute was ruled out for offside.
The Englishman played an inch-perfect pass to Neto for the Blues' opening goal and demonstrated once again that few players are as influential.
Though Palmer did have quiet moments during the match, he still managed to score after carrying the ball from just over the halfway line towards the box.
CHELSEA VS. NEWCASTLE UNITED MATCH STATS
Possession: Chelsea 51%-49% Newcastle United
Shots: Chelsea 17-11 Newcastle United
Shots on target: Chelsea 7-3 Newcastle United
Corners: Chelsea 7-4 Newcastle United
Fouls: Chelsea 13-16 Newcastle United
BEST STATS
WHAT NEXT?
Chelsea play Howe's side again on the Wednesday in the fourth round of the EFL Cup, but this time at St James' Park, before taking on Manchester United in the Premier League on November 3 at Old Trafford.
After they host the Blues, Newcastle are set to take on Mikel Arteta's Arsenal at home in the league on November 2.