Thierry Henry scored his 200th goal for Arsenal to help Arsene Wenger's side end a miserable fortnight on a high note and plunge Blues deeper into Premiership relegation trouble.
The French star produced a typically classy trademark finish after 62 minutes to secure only the Gunners third away league win of the campaign after newcomer Emmanuel Adebayor had struck in the first half.
Arsenal went into the game without eight defenders and a disastrous spell which had seen them exit from the Carling Cup and FA Cup and suffered two league defeats which threatened their hopes of securing a Champions League spot.
On top of that central defender Sol Campbell had been absent since being substituted at half-time in Wednesday's home defeat by West Ham, although his solicitor now claims he will be back in training on Monday.
But in this transitional period Arsenal will always pose a threat when they have Henry, who previously scored his 100th goal for the club against Blues. And Wenger will take heart from the display of Adebayor.
He had only linked up with the Gunners on Wednesday after Togo's elimination from the African Nations Cup but was in the right place at the right time to break the deadlock.
To add to Birmingham's misery striker Emile Heskey was sent off for two bookable offences, the second of which was for a strong aerial challenge on Mathieu Flamini.
The former England player, the seventh City player to be red-carded this season, protested strongly at the Arsenal player and then fourth official Phil Dowd after leaving the pitch.
The breakthrough came after after 21 minutes when Adebayor, a £5million transfer window signing, put the Gunners ahead with his first goal for the club.
Henry's first-time ball played in the over-lapping Abou Diaby and his cross was inadvertently turned by Martin Latka against Taylor but the rebound fell kindly for Adebayor who headed home from two yards.
For all their defensive problems Arsenal still posed a massive threat on the counter-attack and Adebayor squandered a golden chance to double their lead. He found himself with a clear run at goal after racing onto a pass from Reyes but failed to get any power into his shot and Taylor was able to save with ease.
Birmingham looked to build up some momentum at the start of the second period and Fabregas made a timely interception to head clear from Pennant's cross.
Heskey was booked after catching Senderos in the chest when lunging with his foot before, after 62 minutes, Henry put Arsenal firmly in command with his 200th goal for the Gunners.
The France striker pounced on a long ball from Fabregas and rifled a cross-shot past Taylor into the far corner of the net in trademark fashion.
The the home side were reduced to 10 men after Heskey was given his marching orders.