With Arsenal fans once again calling for Wenger to resign during a pre-match protest march outside the Emirates Stadium, the Gunners boss desperately needed a dominant display from his team.
Instead, Arsenal twice had to come from behind to avoid a third successive Premier League defeat.
The north Londoners remain in sixth place, seven points behind fourth-placed City in the fight to qualify for the Champions League via a top four finish.
Arsenal fell behind after only five minutes when Leroy Sane held off Hector Bellerin as he accelerated onto Kevin De Bruyne's pass before rounding David Ospina and slotting home.
Theo Walcott equalised for Arsenal in the 40th minute when he stabbed in after City defender Gael Clichy played him onside following a half-cleared corner.
Just two minutes later, Sergio Aguero restored City's advantage with a predatory finish after more sloppy Arsenal defending.
