Henrikh Mkhitaryan pulled a goal back for the Gunners on 37 minutes and four minutes later set up Super Eagles forward Alex Iwobi to equalize.
Chelsea opened the scoring when summer signing Jorginho, making his home debut, released Marcos Alonso, who raced down the left and squared the ball for Pedro to score with ease.
It came shortly after Arsenal went close to scoring against the run of play when Mesut Ozil shot inches wide after being found by Nacho Monreal’s cross.
After Pedro’s ninth-minute goal, Pierre-Emerick Aubameyang was denied by a near-post save from keeper Kepa and then, a minute before Chelsea doubled their lead, squandered a glorious chance to haul Arsenal level.
Matteo Guendouzi opened Chelsea’s defence with a clever pass out to Hector Bellerin, whose right-wing cross perfectly teed up Aubameyang only for the striker to side-foot over.
It proved to be a costly miss for the Gunners, who were undone again when Morata chased Cesar Azpilicueta’s cross, got the better of Shkodran Mustafi and slotted past former Chelsea keeper Petr Cech.
Arsenal then missed another sitter, this time when Mkhitaryan blazed over after being set up by Iwobi.
But the Armenian atoned with a low, left-footed strike from the edge of the penalty area after Willian had been dispossessed inside the Chelsea half.
Mkhitaryan then turned provider, finding space on the right and sending in a low cross for Iwobi to blast home.
Incredibly, Iwobi missed another great chance for Arsenal in first-half injury time when he fired over after being teed up by Mkhitaryan’s pull-back from the right.