The Gunners left out controversy-hit playmaker Mesut Ozil after his World Cup exertions as 17-year-old midfielder Emile Smith Rowe took centre-stage in Singapore.
Luciano Vietto netted the opener for Atletico against the run of play, but teenager Smith Rowe hit a dazzling equaliser — his first senior goal — in front of new boss Unai Emery as it finished 1-1 after normal time.
The International Champions Cup game went straight to penalties where substitute Atletico goalkeeper Antonio Adan starred, saving three before coolly slotting the winner himself.
Both sides started with unfamiliar line-ups but Arsenal were the dominant force in the first half before they were hit with a sucker-punch four minutes from the break.
In a rare attack from Diego Simeone’s men, Angel Correa picked out his fellow Argentine Vietto, whose header looped past new Arsenal goalkeeper Bernd Leno.
French forward Alexandre Lacazette was denied from close range on three occasions, including a full-length save by Atletico’s Jan Oblak after good work from Smith Rowe.
But Arsenal struck two minutes into the second half when Smith Rowe curled the equaliser into the top corner from the edge of the box, before being mobbed by his team-mates.
Mass substitutions in the last half-hour rid the game of rhythm before the penalty shoot-out victory for Atleti.