A 63rd-minute spot-kick from Jordi Gomez put the Championship side ahead after Mertesacker fouled Callum McManaman but the Germany international pulled his team level with eight minutes of normal time remaining.
Alex Oxlade-Chamberlain – Arsenal's major attacking threat throughout – rattled the crossbar during extra time but Arsene Wenger's men would ultimately hold their nerve to keep hopes of a first major trophy in nine seasons alive.
Arsenal's back-up goalkeeper saved the first two Wigan penalties from Gary Caldwell and Jack Collison, while his team-mates Mikel Arteta, Kim Kallstrom and Olivier Giroud were all on target.
McManaman – man-of-the-match in last season's final – was one of Wigan's inclusions, with manager Uwe Rosler having overseen a 1-0 loss at Millwall on Tuesday with one eye on this showpiece occasion.
Oxlade-Chamberlain was Arsenal's leading light during the opening exchanges and it required a fine save from Wigan goalkeeper Scott Carson to deny Yaya Sanogo – preferred up front to Giroud - from the England man's sixth-minute cross.
Sanogo then prodded over from a Ramsey cross as Wenger's men sought a response, and the French forward was on the receiving end of a superb last-ditch tackle from Stephen Crainey shortly after.
Arsenal ramped up the pressure as Sagna headed against the post from Oxlade-Chamberlain's centre, while Crainey desperately cleared when a header from Kieran Gibbs - on for Monreal - threatened to squirm beyond Carson.
Sanogo displayed fine technique to collect Oxlade-Chamberlain's 97th-minute pass and get a shot away but Carson was equal to the task.
Oxlade-Chamberlain was rarely far away from Arsenal's best moments and thudded a drive against the angle of post and bar with nine minutes of extra time remaining, while Collison wasted a header at the other end.
