Olivier Giroud was sent off for Arsenal as they lost at Dinamo Zagreb in their opening Champions League game.
The Gunners went behind after a Josip Pivaric shot was saved by keeper David Ospina but rebounded in off Alex Oxlade-Chamberlain.
Giroud was then sent-off for a second booking when he fouled Ivo Pinto before Junior Fernandes headed in for Dinamo.
Theo Walcott superbly slotted in to give Arsenal hope but the home side nervously held on for the win.
Walcott had scored a hat-trick at the same Maksimir Stadium for England against Croatia in 2008 but, despite pulling one back, he could not repeat such heroics.
Dinamo held on to extend their unbeaten run to 42 games as they tasted victory over an English top-flight side for the first time in the Champions League.
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