- Watch highlights of the first 90 mins
- Watch highlights of extra-time and penalties
Stand-in goalkeeper Lukasz Fabianski was the hero as his two saves in a penalty shoot-out helped Arsenal beat holders Wigan at Wembley to reach their first FA Cup final since 2005.
After a bright start by Arsenal, it was Wigan who went ahead through a penalty from Jordi Gomez just after the hour.
However the Gunners made it 1-1 with seven minutes left through Per Mertesacker, whose foul had given away the spot-kick.
After Alex Oxlade-Chamberlain had hit the crossbar in extra-time, it was down to penalties.
Fabianski - standing in again for regular number one Wojciech Szczesny - produced fine saves from Gary Caldwell and Jack Collison, before Santi Cazorla rolled in the winning penalty to secure a 4-2 shoot-out success.
Arsenal, who were pushed out of the top four following Everton's win over Sunderland earlier on Saturday, had started brightly.
Oxlade-Chamberlain, passed fit following a groin problem, burst into the Wigan penalty area, but the ball fell through to Scott Carson.
The Wigan keeper then produced a brilliant reaction save to block a bullet header from Yaya Sanogo, the France Under-21 forward handed another start with Olivier Giroud on the bench.
It continued to be one-way traffic during the opening quarter of an hour, but captain Emmerson Boyce marshalled the organised Wigan rearguard well.
On 26 minutes, a corner from Cazorla was knocked down by captain Thomas Vermaelen, which Bacary Sagna blazed across goal when the ball dropped at the far post.
In a rare Wigan attack, Gomez's cross from the left dropped onto the top of the Arsenal net.
Slowly, though, the Sky Bet Championship promotion hopefuls started to gain a foothold in the match
Callum McManaman looked threatening down the right as he chipped an angled shot just over after cutting inside the Arsenal penalty area.
As the match laboured towards half-time, Lukas Podolski curled a tame free-kick wide from a central position 20 yards out.
There was still time for Sanogo to be sent clear, but his first touch was too heavy which saw the ball bobble away and allowed Carson to come out to make another decent block.
It was more of the same following the restart as Arsenal lacked any real penetration in the final third as Wigan maintained their solid shape.
There was then high drama as the hour approached when Wigan were awarded a penalty.
McManaman was again the dangerman, carrying the ball into the Arsenal area, where he was tripped by Mertesacker as the big German stretched to make a sliding tackle.
Referee Michael Olivier had no hesitation in pointing to the spot, although there was a long delay before the kick could be taken as Arsenal full-back Nacho Monreal needed treatement on the far side of the pitch, and was eventually replaced by Kieran Gibbs.
Gomez, though, kept his composure to drill the ball past Fabianski into the top-left corner and sent the outnumbered Wigan fans behind the goal into bedlam.
The Latics had again trived on their underdog status, and suddenly the 50,000 or so Arsenal fans could feel a sinking sense of inevitability about their latest capitualtion when it mattered most.
Wenger made a quick change when he sent Giroud on for Podolski, but the Gunners continued to lack any real fluency.
Arsenal knew time was running out, possibly even on Wenger's long reign, and needed to find a response.
It seemed their fortune had been deserted when first Sagna headed against the post and then Wigan defender Stephen Crainey somehow cleared off the line as Carson palmed Gibbs' header back towards goal.
Finally, though, Arsenal were level on 83 minutes as Mertesacker nodded the ball in following another goalmouth scramble following Gibbs' scuffed shot.
The Premier League side now had the momentum and were camped in Wigan's half looking for a late winner during five minutes of added time, but there was to be no dramatic finale.
Arsenal maintained their possession advantage at the start of extra time, if once more without finding a telling pass to open Wigan up.
Sanogo was denied by Carson again when he turned his marker and drilled an angled shot goalwards, which was palmed over.
On 110 minutes, Oxlade-Chamberlain cut into the right side of the Wigan penalty area and lashed a rising shot against the underside of the crossbar.
There would be no winner, though, as the tie was decided on the lottery of penalties.
Fabianski saved Gary Caldwell's first spot-kick, before Mikel Arteta put Arsenal in control.
Jack Collison, on loan from West Ham, also saw his effort turned away by the Poland keeper and Kim Kallstrom made it 2-0 to the Premier League side.
Jean Beausejour did score, before Giroud tucked his effort into the bottom corner to put Arsenal on the brink of the final.
James McArthur made it 3-2, but Cazorla kept his cool to score and keep the Gunners on course for a first trophy in the best part of a decade.
Watch Per Mertesacker's reaction