Second-half goals from Pedro and Eden Hazard secured a 2-0 win over Bournemouth at Stamford Bridge and ensured we have now taken maximum points from our opening four matches.
The Blues were made to work for this latest victory, with Bournemouth defending well for large spells of the game, particularly in the first half when clear-cut opportunities proved hard to come by. Marcos Alonso striking the post just before the break was the closest we came to an opener.
In the second half, though, we began to offer more of a cutting edge and Pedro, who had only been on the pitch for a few minutes, broke the deadlock with a low finish at the end of an incisive passing move.
Hazard then put the seal on the victory with an angled drive six minutes from time after playing a one-two with Alonso, meaning we head into the international break with 12 points from 12.
Sarri made just one change to the team which beat Newcastle last weekend, and it came in the front three with Willian replacing Pedro.
David Luiz and Toni Rudiger, who was making his 50th appearance for the club, continued alongside each other at the heart of the back four and Mateo Kovacic, who made his first start for the Blues at St James’ Park, retained his place in the side.
Alvaro Morata, fresh from being recalled to the Spain squad yesterday, was once again tasked with leading the line.
For Bournemouth, former Chelsea players Asmir Begovic and Nathan Ake both started.
With the Blues boasting a 100 per cent record going into the game and Bournemouth having taken seven points from their opening three fixtures, both sides approached the contest full of confidence.
A lofted ball over the top from Rudiger almost released Morata inside the opening couple of minutes but Bournemouth captain Simon Francis was on hand to clear the danger, and the visitors then threatened for the first time at the other end with Ryan Fraser supplying a teasing delivery across the face of goal.
Diego Rico, making his first Premier League start for Bournemouth, did well to adjust his body and clear as Willian attempted to get on the end of a smart David Luiz pass, and the Blues were then appealing for a penalty when Willian’s cross, which followed some lovely link-up play between Cesar Azpilicueta, Eden Hazard and the Brazilian, appeared to strike the arm of Jefferson Lerma.
It was a bright start by Sarri’s side, no doubt buoyed by three consecutive wins, but Bournemouth were next to threaten when a David Luiz pass was pounced on by Callum Wilson, who drove towards the Chelsea goal before switching it to Ryan Fraser on his right, but a perfectly-timed tackle by N’Golo Kante, who did superbly to make up ground and get across, took the ball away from the foot of the winger as he was about to pull the trigger.
Sarri’s side were playing some nice stuff, shifting the ball quickly and effectively, and one particular move which began with David Luiz playing out from the back intelligently ended with Jorginho firing just wide from the edge of the box.
As the midway point of the half, however, it remained goalless and although there was no lack of urgency in our attacking play Bournemouth, who had switched to a 3-4-3 system, were defending well.
Eddie Howe’s side passed up a decent opportunity of their own when Wilson, who had raced into the box to meet a cross from the left-hand side by Rico, could only steer his effort over the bar, before both Kovacic and Morata threatened at the other end.
The best opportunity of the game so far then fell our way just before half-time when Kante ran at the retreating Bournemouth defenders before slipping it out to Hazard on the left. The Belgian shifted inside and picked out Alonso, who was unfortunate to see his strike thump the foot of the post.
That proved to be the last chance of the first half, and from our first opportunity after the restart it was Alonso who was denied again when his left-footed drive, from a similar position in which he scored the winner against Arsenal, was beaten away by Begovic.
Bournemouth could, and probably should, have taken the lead moments later when Ake steered his shot over the bar from point-blank range after a corner had been flicked into his path.
Sarri made his first change of the afternoon on the hour as Olivier Giroud replaced Morata, and it was quickly followed by another with Willian making way for Pedro.
Kovacic saw a couple of shots charged down after playing a one-two with Giroud on the edge of the box, before the Frenchman's left-footed volley was deflected behind off Pedro.
As the game entered its final part it was becoming increasingly clear the first goal could be pivotal, and it arrived from the boot of Pedro with 19 minutes left on the clock.
Alonso carried the ball forward and moved it on to Pedro, who exchanged passes with Giroud before skipping past his man and crashing a low drive past Begovic and into the bottom corner.
It was the Spaniard's third goal of the season, a well-taken strike and perhaps the most important so far.
Despite our slender advantage Bournemouth remained a threat, particularly on the break, and Fraser should have done better when he raced through, the Scotsman curling his effort well wide of the far post.
Ruben Loftus-Cheek was introduced for the final 12 minutes, replacing Kovacic in the Chelsea midfield, and the substitute was quickly into the action, driving at the Bournemouth defence and teeing up Pedro, who saw his strike saved by Begovic.
With six minutes left to play, however, the second goal arrived as Hazard raced into the box, exchanged passes with Alonso and drilled his shot beyond Begovic to make it 2-0.
It was the forward's second goal in as many games, and after being eased back into the side following his involvement in the later stages of the World Cup, the brilliant Belgian has enjoyed an influential start to the new campaign.
That was it, and in the end it was a deserved victory for Sarri's in-form side, who now look forward to the visit of Cardiff City in a fortnight's time.
Chelsea (4-3-3): Kepa; Azpilicueta (c), Rudiger, David Luiz, Alonso; Kante, Jorginho, Kovacic (Loftus-Cheek 78); Willian (Pedro 64), Morata (Giroud 60), Hazard.
Unused subs: Caballero, Christensen, Zappacosta, Barkley.
Scorers Pedro 71, Hazard 84
Booked Alonso 32, Kante 54
Bournemouth (3-4-3): Begovic; Francis, Ake, Cook (c); Smith (Ibe 79), Gosling, Lerma (Lewis Cook 87), Rico; Fraser, Wilson, King (Mousset 79).
Unused subs: Boruc, Mings, Surman, Brooks
Booked Gosling 19, Lerma 69
Referee Lee Mason