This was thrilling and excruciating in equal measures, a derby to have the juices flowing, but also a vindication of all the downbeat caution expressed publicly by Maurizio Sarri and Unai Emery through the campaign’s early days.

Chelsea, so relieved to have a player of Eden Hazard’s calibre to fling on and make a difference, triumphed at Arsenal’s expense but, for all the blistering entertainment this derby whipped up, it also provided evidence aplenty as to why these teams are outsiders in the title race.

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The chaos of the opening period summed it up. Whether it was Arsenal obligingly presenting their hosts with a healthy lead or, having revived, carving them open at will only to fluff their lines in front of goal, or Chelsea wilting at the back as if defensive responsibilities had been discarded with Antonio Conte, deficiencies were to the fore.

Sarri declared the last 15 minutes of the first half “horrible” and time in which it would have been “better to go for a cigarette”. The confusion made for a frenzied match but both managers appeared to age in their dugouts at the glorious mess they were witnessing. What ultimately set Sarri’s team apart was the magician on the bench to whom they could turn.

Hazard returned late from the World Cup and had spent most of the contest clad in his tracksuit, trotting up and down the touchline while suffering the goading of the travelling Arsenal fans behind one goal. There had been a period this summer when Chelsea, expecting Real Madrid to formalise interest in their prized asset, had fretted over the 27-year-old’s future at the club.

Sarri had admitted as much on the eve of the game, with Hazard having suggested on the conclusion of Belgium’s World Cup campaign that the time might be right to move on. Yet here he was still in blue, asked to restore some order with 29 minutes remaining, and driving Arsenal deeper and deeper into their shells at the end.

It was his isolation of the visitors’ panicked substitute, Alexandre Lacazette, which was key to coaxing Chelsea’s winner. Hazard darted to the byline far too easily beyond the static forward and, while Arsenal desperately attempted to clutter the penalty area with bodies, Marcos Alonso meandered on to the cutback to finish past Petr Cech.

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Hazard, not content with that impact alone, would force his former teammate into two smart saves in what time remained, and should have supplied Olivier Giroud with another. “I’d rather be out on the pitch than watching from the bench,” he offered through a smile. “But, when I did come on, I did good.”

Life without Hazard is unthinkable, and the club’s priority should be to convince him to buy into Sarri’s project and commit to the club. All that talk of a £300,000-a-week contract has gone rather quiet.

Sarri is already acutely aware of Hazard’s significance to this team’s good health. How Emery, slumping into his dugout as his side were breached for a third time, must wish he had a game-changer who could provide similar gloss to his own work in progress.

Arsenal, soundly beaten by Manchester City last Sunday, have now lost their opening two top-flight fixtures for the first time since 1992, though the new manager will still cling to the positives from this occasion. Some of their approach play in that opening period had been scintillating, and far too good for Chelsea to repel, for all that it was also undermined by profligacy.

They would score twice, through Henrikh Mkhitaryan’s skimmed finish and Alex Iwobi’s shot from the Armenian’s cutback, and took heart from the recovery, but it was the memory of all the misses that lingered.

Facebook Twitter Pinterest Pierre-Emerick Aubameyang reacts after missing an open goal. Less than a minute later Chelsea were 2-0 up. Photograph: Victoria Jones/PA

Pierre-Emerick Aubameyang, Mkhitaryan and Iwobi would all sky shots over the bar from around the penalty spot. Other fine opportunities were spurned by Mesut Özil and Aubameyang – who will surely score far harder chances this season – with such wastefulness combining with uncertainty at the back as to have alarm bells ringing early. There are already question marks over both centre‑halves and whether they possess the pace to thrive in Emery’s high‑press system.

Likewise, discipline was lacking at times. Héctor Bellerín, such a threat in the attacking third, was upfield and absent as Jorginho slid Alonso free early on. The Spaniard’s centre was converted crisply by his compatriot Pedro in the centre.

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Then there was the ease with which Álvaro Morata trundled on to César Azpilicueta’s lofted pass over Nacho Monreal – maintaining the Spanish theme – to score for only the second time in the Premier League since Boxing Day.

“Calm,” preached Emery. “I know we need to improve things and push the players to work. But, for me, the team competed well and had chances in the match.”

Neither side expect to challenge for the title. Sarri admitted that starkly – “No, not in this moment” – in the aftermath of this victorious start to life at Stamford Bridge. Regardless, both these teams will be entertaining to watch.