There was nothing to separate the two sides after a tense opening 45 minutes in Baku, which was played in front of a far-from-full crowd.
However, a 15 minute blitz after the interval brought three goals without reply for Chelsea to effectively seal victory in Azerbeijan.
First was an expert header from Olivier Giroud, who directed Emersons cross past former team-mate Petr Cech in Arsenals goal.
Then Eden Hazard set-up Pedro to double Chelseas lead, before getting in on the act himself by converting from the spot after a foul from Ainsley Maintland-Niles on Giroud after an hour played.
Alex Iwobi emerged from the bench after Hazards goal and got one back for Arsenal almost immediately as he smashed a sensational effort past Kepa from the edge of Chelseas box.
But any hope of a comeback was short-lived as Hazard grabbed his second of the game after playing a one-two with Giroud.