The Blues took a shock lead through Nikola Zigic after 33 minutes as once again we 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 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 us some seven points off the pace, and 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.
We suffered a 3-2 defeat against West Brom in our 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.
We were presented another golden opportunity on 24 minutes when a soft back pass from 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.
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 our 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.
We 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.
Nasri 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 our 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 us 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.
We 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 us 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.