Hopes of another great escape from the Latics were briefly raised as Shaun Maloney's free-kick cancelled out Lukas Podolski's opener, but the shoddy defending which has blighted their season returned as Theo Walcott, Podolski and Aaron Ramsey sealed their fate in a devastating eight-minute spell.
Santi Cazorla had already flashed a header narrowly wide when Roberto Martinez's men switched off horribly at the back from the Spaniard's corner, allowing the ball to bounce on the edge of their six-yard box for the unmarked Podolski to stoop and nod home.
It took until the 25th minute for the visitors to mount a meaningful attack with Laurent Koscielny showing superb alertness and athleticism to clear Jordi Gomez's ball into the box with Arouna Kone looking set to beat Wojciech Szczesny to the ball.
Arsenal were inches away from doubling their lead as the interval approached with Wigan failing to learn the lessons of the opening goal as another Cazorla corner was again left by Per Mertesacker at the near post only for Koscielny to stab wide.
The Gunners will feel Wigan were given a helping hand for their equaliser as Maloney went to ground under minimal contact from Mikel Arteta, but there was no questioning the quality of the forward's finish as he curled a superb free-kick over the wall and beyond Szczesny's despairing dive.
Szczesny was then called upon to produce an excellent save in the opening moments of the second half, racing from his line to spread himself and deny Kone's shot from a tight angle after a neat one-two, before James McCarthy had the ball in the net only to be given offside.
Play switched immediately to the other end and Joel produced a dramatic double-save to keep out Cazorla following good work by Walcott down the flank, with Tomas Rosicky dragging his follow-up effort across the goal and wide.
Wigan suffered a blow when the excellent Callum McManaman was forced out of the action in the 57th minute through injury, with Emmerson Boyce glancing a header wide and then Joel standing up well to a Walcott shot as the drama continued.
But the Latics goalkeeper was powerless to prevent Arsenal from regaining the lead through Walcott in the 63rd minute as Cazorla was given far too much time and space out on the right flank to deliver a precision low cross for the England international to convert from close range.
And the game was up for the Latics just five minutes later as Cazorla's header through found Paul Scharner playing Podolski onside, allowing the Germany international to lift his shot beyond Joel to leave Wigan's players flat on their backs and the visiting fans with heads in hands.
Ramsey ensured Arsene Wenger's men go into their final game of the season at Newcastle on Sunday in pole position to secure the final UEFA Champions League qualification berth as he was released into acres of space on the left before bursting into the box and beating Joel with aplomb.