- Eddie Nketiah (43')
- Youssouf Fofana (31')
Both sides missed chances to win it in an entertaining second half but the result was decided in a shootout with Monaco substitute Takumi Minamino the only player from either side to miss as Aaron Ramsdale stood firm to repel his driven spot-kick.
That left another substitute, Gabriel Magalhaes, with the chance to secure a 5-4 victory for the Gunners and the Brazilian slotted a low finish into Monaco goalkeeper Philipp Köhn's left-hand corner to give Arsenal a morale boost ahead of Sunday's Community Shield clash with Manchester City at Wembley.
Gabriel Jesus was missing with a knee injury, the severity of which will become clear after further assessment. His replacement, Nketiah, was handed the armband in an Arsenal lineup that included new signings Declan Rice and Jurriën Timber while Martin Ødegaard and Bukayo Saka were named among the substitutes.
Monaco started the brighter of the two sides and Aleksandr Golovin forced Ramsdale into a smart eighth-minute save with a low drive from the edge of the box.
The Gunners threatened with several dangerous crossed without testing Köhn and although Gabriel Martinelli looked sharp in the final third, the Brazilian was undone at the other end as the visitors took a 31st-minute lead.
Mohamed Camara took Martinelli on and crossed for Fofana to finish first time past Ramsdale.
William Saliba, who had been booked earlier in the half, benefitted from this being a friendly fixture as he escaped a red card for a cynical challenge on Fofana to halt another Monaco breakaway.
However, Arsenal stirred into life shortly before the break. Rice, a £105 million summer signing from West Ham, was denied his first Gunners goal by a brilliant last-ditch block from Guillermo Maripan before Köhn tipped over Takehiro Tomiyasu's header from the resulting corner.
However, Köhn could do nothing as the subsequent Martinelli corner was turned in by Nketiah from close range at the back post.
Trossard was sent clear inside the final 20 minutes but fired a low effort straight at Kohn before Fabio Vieira fired a volley down into the ground that the Monaco goalkeeper tipped over at full stretch.
The contest was decided by a penalty shootout and after Ødegaard, Jorginho and Havertz all scored, former Liverpool forward Minamino was denied, meaning after Vieira converted, Gabriel was left to enjoy the final word.
- Anthony Taylor