Blues took a shock lead through Nikola Zigic after 33 minutes as once again the Gunners - who had lost their past two league games before the international break - failed to make the most of early possession.
However, Samir Nasri levelled with a somewhat controversial penalty just before half-time, before Marouane Chamakh slotted home a well-taken effort two minutes after the restart which proved enough for all three points.
The win was soured late on, however, when England teenager Wilshere showed his immaturity with a reckless challenge on Zigic which earned him a straight red and a three-match ban.
Defeat at Chelsea last time out had left Arsenal some seven points off the pace, and manager Arsene Wenger had called on his team to produce a strong response from kick-off.
It was almost that as Chamakh went close after just four minutes following a neat one-two with Wilshere on the edge of Birmingham's box, but Stephen Carr blocked his side-foot effort.
Arsenal suffered a shock 3-2 defeat against West Brom in their previous match here last month - and there was more frustration for the home supporters during the first quarter-of-an-hour following some resolute defending by Birmingham.
On 17 minutes, Sebastien Squillaci headed in Samir Nasri's chipped free-kick from the right wing, but the offside flag was quickly up.
Arsenal were presented another golden opportunity on 24 minutes when a soft back pass from former Arsenal midfielder Sebastian Larsson in his own penalty area gifted Gael Clichy a free shot at goal from 10 yards, but the full-back dragged his shot wide of the far post.
Gunners goalkeeper Lukasz Fabianski had not really been troubled, but needed to be alert to collect an inadvertent backward header from Emmanuel Eboue, which was set for the top corner, after a free-kick into the Arsenal box.
The Blues, however, continued to look dangerous from set-pieces and it was no real surprise when the visitors went ahead after 33 minutes.
A throw-in was fed back to Keith Fahey, and his sweeping cross was met by Zigic, who got up above Johan Djourou to power a header back into the bottom corner for the Serbian's first Premier League goal.
Birmingham almost snatched a second when Roger Johnson knocked the ball back across the six-yard box, but Fahey blazed over as he got in the way of Zigic.
Arsenal were then handed a lifeline five minutes before the break when Scott Dann clipped Chamakh's trailing leg and referee Martin Atkinson pointed to the spot.
Nasri made no mistake as he crashed in his fifth goal of the season.
The French winger, though, was soon in the referee's book for barging at Liam Ridgewell, although replays suggested the card could easily have been red after leading with his knee.
Tempers were boiling over as half-time approached, with Blues skipper Carr involved in a heated exchange with the Arsenal bench and Chamakh looked to be on the receiving end of an elbow from Johnson, but it went unpunished.
If there was a touch of controversy about Chamakh's involvement in the equaliser, the Morocco striker produced the perfect response as he put Arsenal ahead just two minutes after the restart.
Wilshere played the ball into the left side of the penalty area, where Chamakh ghosted past Carr before holding off Dann as he rounded the goalkeeper to roll home his fifth goal from a tight angle.
Arsenal soon settled into their usual passing rhythm, as Birmingham suddenly found themselves chasing possession for long spells, but were again guilty of taking too many touches around the box when a more direct approach was required.
Wilshere did just that when charging into the left side of the penalty area before drilling an angled drive over.
Both substitute Tomas Rosicky and Nasri tested Foster from distance while the introduction of Denmark striker Nicklas Bendtner for his first appearance of the season gave Arsenal a different option.
But it will be Wilshere's red card which makes the headlines after he went in late on Zigic, and must now serve a three-match ban.