The understandably nervy win can ease the tension in a weary-looking squad and help Arsenal's push for fourth place and participation in next season's UEFA Champions League.
You could be forgiven for thinking Arsenal actually lost at Wembley, such has been the vitriol from sections of pundits and fans regarding the team's performance.
Yes, the Gunners were pedestrian going forward, but surely, that had to be expected? This is, after all, a squad that has recently endured several damaging defeats and slipped out of contention for the English Premier League title.
It is also a squad ravaged by injuries. Wenger was unable to deploy Mesut Ozil, Tomas Rosicky, Jack Wilshere, Theo Walcott or Laurent Koscielny at Wembley.
No responsible commentator can fail to at least acknowledge this context. Yet even with a threadbare squad lacking in confidence and feeling the pressure, Arsenal were expected to sweep Wigan aside.
Never mind that the Latics were the current holders and had knocked out Manchester City at the Etihad Stadium in the previous round.
The truth, even though the critics will be loath to admit it, is that semi-finals rarely work that way. Cup competitions play by different rules.
That is particularly true of the FA Cup. The fabled competition is imbued with the charm and romance of so-called "lesser" teams upsetting the natural order.
Don't believe me? Well let's consult Wenger's history at this stage of the FA Cup. The French boss has been victorious in five other semi-final clashes, three of which were particularly telling.
In 1998, Arsenal bested championship side Wolverhampton Wanderers by a solitary goal. The scorer was deputy striker Christopher Wreh, proof that Wenger has played backup forwards in semi-finals in the past.
This was the double-winning team of 1997/98, perhaps the most balanced and powerful Arsenal team Wenger has ever assembled. Yet even they scraped past a lower-league opponent.
The following season, Arsenal's title chasers needed a miracle save from David Seamen and a lone goal from Freddie Ljungberg to see off First Division battlers Sheffield United.
So there's three semi-finals against opponents Arsenal were expected to comfortably overcome, two of whom played in a lower division. Yet none of those games proved comfortable.
The point is, semi-finals are there to be won. Doing it via football with a flourish is a bonus.
Winning this semi-final will have given Arsenal a massive confidence boost. It's one that can inspire them to overturn Everton and secure fourth place again.
That will require a strong finish, probably wins in each of the last five league fixtures, a run similar to last season. But repeating last season's heroics would be harder without the promise of another day at Wembley.
This squad, largely the same as the 2012/13 version, may not summon the same enthusiasm for fourth place when that is all that is left to aim for.
Being in that identical position one year on represents a depressing form of repetition. But now these players know they have a tangible chance to land an actual trophy this season.
I want titles and that is why I came to Arsenal. Every football player wants to win titles. We’ve gone many years without winning one. And if not, what I’ll look for in my next destination is to have the chance to win.
The club's record-signing Mesut Ozil came to North London to claim silverware. Now he has extra motivation to return from injury in his very best form:
The chance to lay hands on a trophy for the first time since 2005 won't go away even if Arsenal falter in the league. That removes an element of the pressure surrounding the next five games.
A more relaxed atmosphere within the squad can help Arsenal play more freely. That will be crucial in restoring the fluency and audacity to the team's game.
Those qualities have been sorely missing in recent matches, particularly at Wembley. The negativity borne from yet another collapse in a title race has obviously stifled the creative daring of several players.
With some of the pressure off, the likes of Cazorla, Aaron Ramsey and others can revive Arsenal's commitment to expansive, technically proficient attacking football.
While a solid defensive shape will be vital in the final games, Arsenal's ability to create more chances will be just as important.
In fact, there was evidence against Wigan that the Gunners are steadily recovering their sound defensive base. They held their shape well throughout the contest, successfully restricting their opponents' own lauded passing style.
Arsenal became a little disjointed once Wenger switched to 4-4-2 and went direct, but the object then was to chase the game.
On a side note, Wenger deserves credit for his tactical and philosophical shift a goal down. Partnering Yaya Sanogo with Olivier Giroud gave the Gunners a genuine aerial advantage over a team set up to close spaces between the lines.
But don't count on Wenger getting any credit. Any other manager would be lauded, but Wenger's Plan B—yes, that's right, Plan B—will only be viewed as desperate.
One semi-rant aside, Arsenal's more compact defensive showing bodes well for the race for fourth. The next step has to be offering more of a threat going forward.
That task will be helped by getting healthier. Arseblog News has reported that Ozil, Rosicky and Koscielny were all be part of first-team training Monday.
Surviving a scare at Wembley by grafting their way to an ugly win has released some of the tension around Arsenal.
With more players returning from injury, and the confidence the win at Wembley inspired, the Gunners can now play with enough freedom to overhaul Everton.