Chelsea had appeared to have adapted quickly to Sarri's famously expansive style of play, winning their opening two league games after being well beaten by Manchester City in the Community Shield.
However, they came up against a stubborn and well-organised defence at St James' Park and struggled to break Newcastle down despite a dominance of possession that bordered on the ridiculous.
The visitors were handed a huge boost 14 minutes from time as referee Paul Tierney ruled Fabian Schar had fouled Marcos Alonso in the box, despite replays suggesting the Switzerland international had got his foot to the ball.
Eden Hazard, making his first start for Chelsea since helping Belgium to the semi-finals of the World Cup, dispatched a confident penalty, although Martin Dubravka got a fingertip to the ball.
It was Chelsea's turn to feel aggrieved when Yedlin appeared to elbow Olivier Giroud in the build-up to Joselu heading in a near-post equaliser, but the American handed Chelsea three points by inadvertently turning in Marcos Alonso's first-time effort.
Hazard twice required treatment in the opening 20 minutes but was able to continue and flashed an effort wide of the right-hand post.
Newcastle eventually offered a response as Salomon Rondon headed wide, yet Pedro spurned two chances to put Chelsea ahead, with Hazard continuing to pull the strings for no reward.
Azpilicueta was able to test Dubravka shortly after the restart as he latched on to a lay-off from Pedro. Antonio Rudiger then blasted against the crossbar with a vicious long-range effort before Hazard made the most of Tierney's contentious call.
Giroud was soon the man asking questions of the officials after Joselu's header just beat the hand of Courtois, yet the World Cup winner played a part in the decider as Alonso latched on to his knock down and Yedlin made the crucial error.
What it means: Chelsea show they can win the hard way
While this Chelsea showing was far from vintage 'Sarri-ball', it proved they can tough out results when needed. They had a helping hand with the penalty, but Sarri will care little about that after seeing his side join Liverpool and Watford at the top of the table, two points clear of defending champions Manchester City.
Pat on the back: A happy return for Hazard
While the metronomic Jorginho completed more passes than the entire Newcastle side, it was Hazard who was at the heart of everything for Chelsea, with his well-struck spot-kick the least his performance merited.
86 - Jorginho completed 86 passes out of a possible 92 in the first half (93.5%), 19 more than the whole Newcastle side combined (67). Circles. pic.twitter.com/3SxjTyVTxE— OptaJoe (@OptaJoe) August 26, 2018
Boot up the backside: Luiz endures another lapse
Often criticised for lapses in concentration at the back, David Luiz was at fault for Newcastle's leveller as he stood still and allowed Joselu to steal in and meet Yedlin's delivery. Chelsea may be unbeaten, but defensive vulnerabilities have been laid bare in their last two games.
Key Opta facts
70 - Eden Hazard’s goal was his 70th for Chelsea in the Premier League - overtaking Jimmy Floyd Hasselbaink in third (69); only Frank Lampard (147) and Didier Drogba (104) have scored more for the Blues. Special. pic.twitter.com/ARNDX2xTvm— OptaJoe (@OptaJoe) August 26, 2018
Chelsea have registered their first Premier League victory at St James' Park since December 2011, after drawing one and losing four of their previous five visits.
Joselu's goal in the 83rd minute came from Newcastle's first shot on target since the sixth minute and their only shot on target in the second half.
Jorginho completed 158 passes out of a possible 173 (91.3%), 27 more than the whole Newcastle side combined (131).
Chelsea welcome Bournemouth to Stamford Bridge next weekend as they look to maintain their unbeaten start. Newcastle's attention turns to the EFL Cup and a visit to Nottingham Forest on Wednesday before the substantially more daunting trip to City.