Marcos Alonso's late strike settled a chaotic classic in Chelsea's favour after Arsenal fought back from two goals down and threatened to earn a point at Stamford Bridge.
Maurizio Sarri's side built that advantage inside the first 20 minutes after Pedro turned in Alonso's cross and Alvaro Morata added another seconds after Arsenal's Pierre-Emerick Aubameyang blazed over from close range.
Henrikh Mkhitaryan wasted a similar opportunity before pulling one back with a low shot that Chelsea's new £71m keeper Kepa Arrizabalaga should have saved before Alex Iwobi put the Gunners on level terms.
Aubameyang and Iwobi missed further chances before half-time before Chelsea controlled the second half, Alonso sweeping in substitute Eden Hazard's cross nine minutes from time to make it successive wins for Sarri and two defeats for new Arsenal manager Unai Emery.
This was a heavyweight Premier League clash for the managerial newcomers Maurizio Sarri and Unai Emery - and they were provided with plenty of food for thought after an engrossing 90 minutes.
Emery is perpetual motion in his technical area, pacing it constantly from almost the first minute, a blur of gesticulations and dramatic effect with cajoling and encouragement throughout.
The Spaniard is still trying to put his imprint on this Arsenal team after the end of Arsene Wenger's 22-year reign and he is very obviously a hands-on figure.
It is also clear from the manner in which Arsenal got back into the game - even though they ended defeated - that his new players are fighting for their manager.
Sarri, dressed casually in a t-shirt and tracksuit bottoms, was far less animated than Emery but was still keen to get his message across and it is already clear he is determined to repeat the brand of attacking play that made his reputation as he makes his mark at Stamford Bridge.
These two experienced managers will add plenty of character and colour to the Premier League's A-list cast of managers - and both will have much to keep them occupied.
Source: BBC