Santi Cazorla scored the decisive spot kick to put Arsenal into the FA Cup final for the first time since 2005 while Wigan's dream of retaining the trophy ended after Gary Caldwell and Jack Collison had their penalties saved by Lukasz Fabianski.
Wigan took the lead after 63 minutes when Jordi Gomez scored from the spot, needing nerves of steel to score his penalty as he had to wait for three minutes while Arsenal defender Nacho Monreal received treatment.
When he finally did step up Gomez planted his left-foot shot wide of Fabianski who dived the right way but could not reach it. Per Mertesacker had conceded the penalty with a lunging foul on Callum McMananam to leave Arsenal staring at another season without any silverware.
Arsenal equalised after a period of sustained pressure in the 82nd minute which saw Bacary Sagna hit the post, Scott Carson save brilliantly from a Kieran Gibbs header and then Stephen Crainey clear off the line.
Mertesacker made up for conceding the penalty by beating the offside trap to glance his header home from close range.
Arsenal will face the winners of Sunday's semi-final between Hull City and Sheffield United in the FA Cup final at Wembley on May 17.
