The Blues took the lead through Eden Hazard's penalty after Marcos Alonso was fouled by debutant Fabian Schar but substitute Joselu equalised for Newcastle with his second goal of the season.
Chelsea, though, went straight up the other end and a DeAndre Yedlin own goal, from Alonso's shot, sealed another three points to take them level with Liverpool at the top of the table.
Standard Sport's Dan Kilpatrick picks out the key talking points from St. James' Park...
Sarri start continues despite Newcastle efforts
Sarri has said that it could take three months for Chelsea to adapt to his style of football and this was very nearly a first setback for the Italian coach following the wins over Huddersfield and Arsenal.
Chelsea enjoyed over 80 percent of possession but, in the end, they had a contentious Hazard penalty and Yedlin's own goal four minutes from time to thank for victory.
Newcastle, playing an unadventurous 5-4-1 system, frustrated the visitors for long periods and the worry for Sarri is that other lesser clubs could copy the Magpies' blueprint and stop his side with numbers behind the ball and bodies in the centre of the pitch.
For all Chelsea's pretty passing, there was a worrying lack of cutting edge and Newcastle's equaliser through substitute Joselu was not entirely undeserved given the penalty-box action, if not the general play.
Hazard shines again for Chelsea...
For much of this game, there was nothing to declare except Hazard's genius. The Belgian winger made his first start of the season but, for a while, it looked like he would not see out the first half after being caught by Matt Richie after 50 seconds and then again by Mo Diame.
After receiving treatment for Diame's challenge, Hazard gingerly returned to the pitch and, as is so often the case, seemed galvanised by Newcastle's roughing-up.
Playing on the left wing but drifting around the entire Newcastle half, he fired wide twice in quick succession after Diame's tackle and created Chelsea's best chance of the first half, driving into the box and squaring for Pedro, whose low shot was saved.
It was no surprise that he played to Alonso, who drew a a foul from Schar for the penalty, before stepping up to cooly convert it. He is truly the difference-maker for Chelsea, particularly in games like this one.
...but Morata does not
Perhaps this won't come as a massive surprise but Alvaro Morata was ineffective and meek. Faced with Newcastle's dour, defensive tactics, Chelsea needed a committed performance from the centre-forward but, too often, he was a yard behind the action – or nowhere to be seen at all.
He was hooked just after the hour for Olivier Giroud – it may be time to start the World Cup winner – having had no shots on target – both his efforts were easily blocked – and completed no key passes.
On paper at least, Morata appears to have all the qualities to be a success in the Premier League but, whether due to confidence or something else, it has not translated onto the pitch. Sarri's job is to change that but, for now, Morata feels like a weak link, particularly considering the quality of Chelsea's midfield and wingers.
Jorginho Chelsea's new main man
Three games into the new season and it is already clear that N'Golo Kante is no longer the most important player in Chelsea's midfield, as he has been in the previous two seasons.
That is now summer signing Jorginho, Sarr's midfield metronome. Just as against Huddersfield and Arsenal, Jorginho pushed Chelsea forward at every opportunity with one- or two-touch passes, with everything going through the new No.5.
He was just as dominant when Chelsea did not have the ball – at one point early in the second half screaming at Pedro to press higher up the pitch. At least until the rest of the squad adapt to Sarri's methods, Jorginho is very much the coach's on-pitch general and pivotal to their success.
Lascelles absence overshadows defensive Newcastle display
The official line from Newcastle and Rafa Benitez was that captain Jamaal Lascelles was missing from the squad with an ankle injury but reports suggested he had been dropped following a row with Benitez over the manager's decision to revert to three centre-backs.
The Spaniard was expected to be asked about the issue post-match but, whatever the truth, his decision to switch to a back five nearly paid off.
Debutants Federico Fernandez and Schar helped to flood the centre of the pitch, frustrating Chelsea for long periods, while Newcastle used the pace of Yedlin effectively on the counter-attack.
But this was a hyper-negative way to play at home, with Salomon Rondon and then Joselu often completely isolated and helpless up front. Given the players available to him – Jonjo Shelvey was injured and Kenedy ineligible – Benitez will say he had no choice but it was testament to how difficult this season will be that the manager felt the need to play such a negative game.