The Gunners were heading for defeat at the Aviva Stadium until substitute Alexandre Lacazette struck with the last kick of the game.
The first 10 penalties were all scored before Petr Cech saved from Ruben Loftus-Cheek.
Both sides produced a perfect set of five penalties each to send the shootout to sudden death.
Here’s Arsenal player ratings according to football.london.
Goalkeeper: Petr Cech - 8
Petr Cech was Arsenal's hero against his former club Chelsea as Unai Emery's side triumphed 6-5 in a penalty shoot-out after a tremendous 1-1 International Champions Cup draw in Dublin.
Right-back: Hector Bellerin – 4
Without his speed as a crutch, he looked very ordinary in defence.
In the second half and got more involved going forward.
Centre-back: Shkodran Mustafi – 5
The German found himself out muscled by Morata at times but found his range more in the second half as the Blues didn’t trouble in the last half hour.
Centre-back: Sokratis Papastathopoulos – 5
his partnership with Mustafi is still young and they certainly seemed more comfortable together in the second half.
Left-back: Sead Kolasinac – 6
Going forward, he was industrious if not very creative but had two great chances to get Arsenal on the scoreboard.
Midfield: Mohamed Elneny – 5
The Egyptian got caught high up the pitch on more than one occasion after failing to execute a press on the Chelsea defence.
Midfield: Matteo Guendouzi – 7
The 19-year-old was a disruptive force in defence and kicked off an attack or two of his own
Midfield: Emile Smith Rowe – 4
He Made a superb run and offload to give Kolasinac a chance late in the first half but for the most part, he looked like a teenager playing with men.
Attacking midfielder: Henrikh Mkhitaryan – 6
Mkhitaryan made more of an impact in the second half as Arsenal gained more control in attack but failed to find the breakthrough.
Attacking midfielder: Mesut Ozil – 7
Ozil failed to control proceedings to the degree that he is expected to and grew into it more in the second half casing some headaches for the opposition.
Striker: Pierre-Emerick Aubameyang – 5
Auba failed to take his chances when they did come. he missed the ball completely when played in behind by Mkhitaryan. The second half was no more fruitful for the Gabon striker as he was eventually replaced by Lacazette.
Substitutes
Alex Iwobi (on for Smith-Rowe): 8
Iwobi immediately made an impact, giving Arsenal a more direct form of attack. He scored the winning penalty to seize victory for Arsenal.
Ainsley Maitland-Niles (on for Kolasinac): 6
Maitland-Niles was forced into action at full-back once more when Kolasinac went off injured.
Reiss Nelson (on for Mkhitaryan): - 7
Nelson trouble through the heart of the Chelsea defence. Nelson looks at his best when he cuts inside from the wing and plays quick one-twos with either an overlapping full-back or a supporting midfielder. Found Lacazette for a late, late leveller.
Alexandre Lacazette (on for Aubameyang): - 8
Brilliant reaction and placement to score in the final seconds of the game and salvage a draw.
Calum Chambers (on for Bellerin): - 8
He handled Hudson-Odoi easily and showed superb confidence on the ball.
