Having knocked out Manchester City in the previous round, Wigan's FA Cup fairytale looked set to continue when Jordi Gomez opened the scoring from the penalty spot in the 63rd minute after Callum McManaman had been brought down by Per Mertesacker.
However, Mertesacker made amends with just eight minutes of normal time remaining to head home at the back post and keep the tie going for another half hour.
It eventually came down to a shoot-out and Wigan's brave defence of the FA Cup was eventually brought to an end as Lukasz Fabianski saved penalties from Gary Caldwell and Jack Collison in a 4-2 victory.
Arsenal had started brightly. Alex Oxlade-Chamberlain, passed fit following a groin problem, burst into the Wigan penalty area, but the ball fell through to Scott Carson.
Carson 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 Santi 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, Wigan 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 area.
As the match laboured towards half-time, Lukas Podolski curled a tame free-kick wide from 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 danger man, 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.
Arsene 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 Stephen Crainey somehow cleared off the line as Carson palmed Gibbs' header back towards goal.
Finally, though, Arsenal were level on 82 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.
In extra-time, Oxlade-Chamberlain cut into the right side of the Wigan area and lashed a rising shot against the woodwork.
There would be no winner, though, as the tie was decided on penalties.
Fabianski saved from Caldwell and Collison and there was no way back as Arsenal scored four out of four, with Cazorla's strike sparking the celebrations.