Goals from Chelsea's Victor Moses and Arsenal new boy Sead Kolasinac sent the game to a shootout.
Goalkeeper Thibaut Courtois and star signing Alvaro Morata were the Chelsea fall guys as Arsenal won the Community Shield 4-1 on penalties at Wembley on Sunday.
Goals from Chelsea's Victor Moses and Arsenal new boy Sead Kolasinac sent the game to a shootout and with both Courtois and Morata limply squandering their spot-kicks, Arsenal won the trophy for the third time in four years.
Courtois blazed his penalty over the bar before substitute Morata, a £58 million (£75.6 million; 64.2 million euros) capture from Real Madrid, shot wide, allowing Olivier Giroud to seal victory for Arsenal.
Arsenal, embarking upon their first season without Champions League football since 1997, have won on their last nine visits to Wembley, a run stretching back to a victory over Wigan Athletic in the semi-finals of the FA Cup in 2014.
Arsene Wenger's side open the Premier League season at home to 2016 champions Leicester City on Friday, with Antonio Conte's Chelsea beginning their title defence at home to Burnley the following day.
Moses, sent off after receiving a second yellow card for diving as Arsenal stunned Chelsea 2-1 in May's FA Cup final, partially atoned by putting the champions ahead early in the second half.
But after Pedro had been shown a straight red card for an ugly challenge on Mohamed Elneny, Kolasinac headed in an 81st-minute equaliser to leave the game 1-1 at full-time.
As in the cup final, Arsenal made the more assured start and came within inches of opening the scoring when new signing Alexandre Lacazette curled a shot against the post after a slick counter-attack.
Per Mertesacker was one of the heroes of Arsenal's FA Cup win, expertly marshalling a badly depleted defence, but the club captain was to last just 27 minutes of the teams' reunion.
The giant German centre-back had to go off after a collision with Gary Cahill's elbow left blood streaming down his face, giving Bosnian defender Kolasinac an opportunity to make his official debut.
As Arsenal reorganised, Chelsea began to assert themselves, Moses and Pedro working Petr Cech before Willian was harshly booked for diving after his left foot was clipped by Hector Bellerin's knee inside the box.
Neat footwork set Alex Iwobi up to curl a shot at Chelsea goalkeeper Courtois late in the first half, but within a minute of kick-off in the second half, Arsenal found themselves behind.
Granit Xhaka's attempt to clear Willian's corner sent the ball high into the air and when Cahill headed it back into the danger area, Moses darted in behind Rob Holding to apply an emphatic finish.
Elneny squandered a presentable chance for Arsenal by slicing wide and then sent Courtois scrambling with a mishit cross from wide on the right.
Wenger threw on Giroud and Theo Walcott for Lacazette and Iwobi and saw Xhaka extend Courtois with a 30-yard effort.
Pedro's dismissal for catching Elneny's left Achilles with his studs tipped the momentum in Arsenal's favour and they equalised when Xhaka's cross from the ensuing free-kick was headed in by Kolasinac.