Record signing Morata – a late substitute – dragged a poor effort wide moments after goalkeeper Thibaut Courtois had blazed over in a first use of a new penalty shootout system.
Premier League champions Chelsea had gone ahead through Victor Moses, before Pedro was sent off for an ugly lunge on Mohamed Elneny.
From the resulting free-kick, debutant Sead Kolasinac headed the Gunners level to take the match to penalties.
The shootout – the first in English football to follow the ABBA format – saw Chelsea miss back-to-back penalties to allow Olivier Giroud to win the match from the spot.
Level at 90 minutes, the match went straight to penalties, which were taken in the ABBA format.
Designed to prevent a perceived advantage to the team going first, the system sees team A take the first kick followed by team B – before team B go again. Team A then get two successive penalties, a little like the tie-break in tennis, and so on until there is a winner.
Confused? You are not alone as not even the players seemed to understand.
After Gary Cahill’s opener for Chelsea was cancelled out by Theo Walcott, Arsenal defender Nacho Monreal stepped forward, correctly, to take his kick. However he was waved back by several of his Gunners team-mates, who seemed confused by the new format.
Monreal scored, before Courtois and Morata both missed horribly, to the delight of the Arsenal fans behind the goal.
That allowed first Alex Oxlade-Chamberlain and then Giroud to score and start the Arsenal celebrations.