Robin van Persie and Abou Diaby had fired the Gunners into a 2-0 lead inside 18 minutes.
However, Lee Bowyer capitalised on a mistake by young keeper Vito Mannone - preferred to fit-again Manuel Almunia - to pull a goal back before half-time.
After soaking up plenty of pressure during the second half from the battling Blues, Andrey Arshavin wrapped up the points late on as Arsene Wenger's side made it seven successive victories in all competitions this season.
New Birmingham owner Carson Yeung - who has promised manager Alex McLeish a transfer kitty of up to £40million to spend in the January transfer window - was in the stands.
However, the challenge ahead to make his club in the same league as the Gunners was clear inside the opening few moments as the hosts immediately went on the offensive.
Emmanuel Eboue combined with Theo Walcott down the right to swing over a dangerous cross towards Robin van Persie.
On five minutes, the Dutchman knocked down a high ball into the path of Tomas Rosicky at the edge of the penalty area.
However, the Czech midfielder scuffed his first-time shot into the ground.
Birmingham defender Liam Ridgewell left Walcott - making his first start of the season following a back problem - in a heap following a strong sliding challenge.
The Arsenal forward, though, bent his knee back when falling, and had to go off for extended treatment.
As play continued, the home side should have taken the lead when Diaby's left-wing cross was knocked back by van Persie at the far post, but once again Rosicky got his timing all wrong and failed to make a decent contact.
Walcott, hoping to be part of Fabio Capello's World Cup squad, soon came on again - immediately picking up the ball on the right, expertly side-stepping Ridgewell before his cross was tipped over by Joe Hart.
The opening goal finally came on 16 minutes.
Alex Song collected possession 25 yards out, and slipped a lovely low pass through the left side of the penalty area.
Van Persie took the ball on his right, then switched back inside past Stephen Carr before drilling it into the far corner.
Before Birmingham could recover, it was 2-0.
Eboue put Rosicky clear down the right channel, and his cut-back from the near post went all the way through to Diaby - who smashed a first-time effort into the roof of the net.
Arsenal were now in cruise control, but to their credit, Birmingham maintained some tempo.
Song bundled over James McFadden to concede a free-kick in a decent position for the visitors, some 25 yards out.
Larsson, who left Arsenal in January 2007, struck his effort well as it beat the wall, but Mannone got down quickly to make the save.
Walcott eventually had to go off, replaced by Arshavin on 33 minutes.
Arsenal were made to pay for a lapse in concentration as Birmingham pulled a goal back after 38 minutes.
Barry Ferguson sent a deep cross into the penalty area, which Diaby flicked back up in the air.
Mannone, under pressure from Larsson, came to collect, but dropped the ball - which Bowyer smashed into the net.
Arsenal quickly looked to restore their two-goal cushion, and Hart saved well down at the right-hand post to deny Arshavin.
Birmingham, clearly boosted by their goal, had an early chance at the start of the second half when the ball flashed across the Arsenal six-yard box.
At the other end, Arshavin stabbed a close-range effort wide after Diaby's low centre.
Larsson was, at full stretch, penalised for what referee Lee Probert deemed a somewhat harsh backpass, giving Arsenal an indirect free-kick eight yards out.
Fabregas rolled the ball to Arshavin, who stopped it for van Persie, but the Dutchman's fierce effort skimmed off the top of the crossbar.
As the hour passed, Arsenal maintained the pressure, but despite all of their decent approach play, failed to find a telling pass.
It could have proved costly as Mannone made a brave take as Ridgewell's pass went through the Arsenal six-yard box, which would only have needed a touch for the visitors to equalise.
Arshavin, however, settled matters with five minutes left when he slotted home from just inside the penalty area after a quick counter attack.