Former Newcastle striker Martins swept home after a terrible mix-up between goalkeeper Wojciech Szczesny and centre-half Laurent Koscielny.
It was, though, no more than Blues deserved following a battling display as Arsenal, without injured captain Cesc Fabregas and England winger Theo Walcott, once again failed to deliver when it mattered most.
Nikola Zigic had headed Birmingham in front on 28 minutes, but Robin van Persie equalised with a fine volley.
The Arsenal fightback, though, failed to materialise as Arsene Wenger's men could not make the most of their possession and were dealt a killer blow when Szczesny spilled Zigic's knockdown after Koscielny's mis-kick and Martins slotted home in front of the Blues fans to send the Midlands club into Europe.
Arsenal were crestfallen at the final whistle, but Wenger must now lift his side for an FA Cup fifth-round replay against Leyton Orient before the return leg of their Champions League last-16 clash against Barcelona to ensure another season which promises so much does not fail to deliver.
There was something of a sense of justice being done after a poor offside call inside the opening two minutes should have seen Arsenal reduced to 10 men and Birmingham awarded a penalty.
Lee Bowyer ran from behind the last defender onto Craig Gardner's pass before rounding Szczesny, who brought him down.
However, instead the assistant's flag went up and the Gunners went unpunished.
Arsenal slowly started to find their passing game as Andrey Arshavin's shot was blocked by Ben Foster.
Samir Nasri then weaved through three markers into the right side of the Birmingham box, but fired into the sidenetting.
The Blues looked to unsettle Arsenal in possession, and Martin Jiranek made a fine tackle as Arshavin broke down the left.
The Gunners, not for the first time, found themselves trying to break down two banks of four as Birmingham settled into a disciplined rearguard action.
Some careless possession, though, saw Birmingham break and Koscielny had to be alert to head the ball behind after it was swung into the Arsenal penalty by Keith Fahey.
It proved costly as from the resulting corner, Zigic nodded the Blues in front on 28 minutes after Roger Johnson headed the ball back into the six-yard box.
Arsenal almost responded immediately when van Persie sent a flying header over the bar from Bacary Sagna's cross.
Giant Serbia striker Zigic almost doubled the Blues' lead when Gardner touched the ball through from the edge of the box, but this time Szczesny was out quickly to make a smart block.
Arsenal were rattled, with Johan Djourou heading over his own crossbar, but after weathering the storm they were level on 39 minutes.
Wilshere broke quickly down the centre and when the ball came back to him at the edge of penalty area, the England midfielder crashed a 20-yard effort against the crossbar.
Arshavin picked up the rebound, turning it back into the six-yard box where van Persie volleyed the ball into the left-hand corner.
The Dutchman then needed treatment after kicking Roger Johnson's leg in the process of scoring, and jarring his knee.
Fortunately for Arsenal, with the return leg against Barcelona less than two weeks away, van Persie, skipper in Fabregas' absence, was soon back in the action.
The Gunners continued on the offensive going into the break, and Nasri's 25-yard effort was well saved by Foster.
Tomas Rosicky almost put Arsenal ahead at the start of the second half when he arrived late at the edge of the area onto a Sagna cross, but his volley flew just wide.
Despite all of their possession, Arsenal were almost undone again when Fahey crashed a 20-yard effort against the inside of the post.
As the hour mark passed, Birmingham continued to disrupt Arsenal's flow in midfield.
Arsenal withdrew van Persie, perhaps as a precaution, on 70 minutes, replacing him with Nicklas Bendtner, who enjoyed a productive loan spell at Birmingham in the 2006/2007 campaign.
Nasri's shot was blocked by Foster following a quick Arsenal counter-attack, with the Birmingham keeper then denying Bendtner.
Foster was in action again to claw away Nasri's 25-yard effort.
However, disaster struck for Arsenal with just a minute left when Zigic's knockdown was spilled by Szczesny as Koscielny missed his clearance.
Substitute Martins swept the loose ball into an empty net to secure a famous victory for Birmingham and prolong Wenger's six-year quest for a trophy.