The Blues were looking comfortable after going two up inside half an hour, with Arsenal’s woeful defending clearly a source of frustration to Unai Emery on the sideline.
Pedro scored the first for Chelsea, turning in a cross from Marcos Alonso, with his strike then followed up by Alvaro Morata opening his season’s account.
As Chelsea looked like they were about to dominate the game, Arsenal fired back with two goals.
Henrikh Mkhitaryan scored the first in the thirty-seventh minute and Alex Iwobi levelled the match just before half time.
Despite being absolutely battered, Arsenal could even have gone in 5-2 up at the break but Aubameyang, twice, and Mkhitaryan were guilty of missing eight-yard sitters.
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And they were made to pay the price when Chelsea’s continued dominance after the break led to Alonso finally settling matters late on.
What a game this was.
Or, more specifically, what a first half.
Arsenal were absolutely woeful, seemingly even more bemused by their new manager’s tactics than they had been in his first game.
And as awful as they were, Chelsea were excellent with each and every one of his players responding exactly how their new boss wanted them to.
They took the ball from Arsenal at will and twice in the first four minutes turned over possession within seconds of Petr Cech rolling the ball out from a Gunners’ goal-kick.
Even at that early stage, a goal was so obviously coming and, sure enough, the home side were soon ahead.
Alonso found Willian, who in turn fed Jorginho, and when his delicious pass inside Henrikh Mkhitaryan picked out Alonso’s forward run, his low cross was all the invitation Pedro needed to put Chelsea ahead.
Chelsea were in such control that perhaps it was a little over-confidence that saw them open up for Shkodran Mustafi to slip a good ball through to Aubameyang but his effort was straight at Kepa Arrizabalaga.
Then, moments later, the Gabonese missed the first of two gilt-edged chances after Matteo Guendouzi’s brilliant pass released Hector Bellerin, blazing over with the goal at his mercy.
Aubameyang must have wanted the ground to swallow him when the goal-kick was rolled out to Cesar Azpilicueta and he pumped a long ball forward to Morata, who held off Mustafi and tucked a smart finish past Cech for the second.
Things went from bad to worse for Arsenal when Mkhitaryan blasted over and Emery and his men looked to be in for a long afternoon.
Suddenly, though, they got the break they’d been looking for when Mkhitaryan’s low drive beat Arrizabalaga despite him getting a hand to it.
And before the break, Iwobi scored what had looked a very unlikely equaliser.
The half still wasn’t done with Aubameyang somehow missing another effort with the goal at his mercy.
Sarri must have been furious, but whatever he said to his men clearly did the trick as they soon took control again.
Not as they had done before the break but still they spent most of the second period in Arsenal’s half.
Chances were few and far between at either end and the first real save Cech had to make was from a David Luis free-kick which tested him nicely.
But there was little the former Chelsea keeper could do when Eden Hazard, on as a substitute, sent over a low cross which Alonso tucked home.
It was a win Chelsea deserved but despite the smiles from Sarri one they nearly threw away.
Still, it’s two wins from two for the Italian and very positive in south-west London.
That isn’t the case in north London for Emery, though, who faces another week of tough questions.