The Saints dazzled for long periods of the game, notably the opening 30 minutes where they raced into a two-goal lead to silence Stok Cae Ras.
Having been hit with two hefty early blows and surviving a few other scares, Phil Parkinson's men regrouped rather impressively and showed they have no intent on giving up sixth spot without a fight.
Josh Windass netted his 13th goal of the campaign to get the hosts back into the contest, putting himself level with previous top scorer Kieffer Moore this term in the process.
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But after delivering a brutal sucker punch on the hour mark when Cyle Larin intercepted a Lewis O'Brien pass before breaking free to score the Saints' third, Tonda Eckert's men struck twice again late on to put the gloss on a remarkable night's work for the visitors.
It meant Southampton are now unbeaten in 16 games across all competitions and have won each of their past five games - including Saturday's astonishing FA Cup quarter-final triumph over Premier League leaders Arsenal at St Mary's Stadium.
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The overriding feeling among those of a Wrexham persuasion was that they had simply been outplayed by a better side. In truth, it is hard to argue otherwise.
It ultimately ensured Eckert's side moved above the Red Dragons into the fourth and final play-off spot, while they also have a game in hand over those around them.
So Wrexham's top six hopes are now over. Put simply, they've blown it.
This is at least what some neutrals or Wrexham 'haters' are saying. But the reality is, they couldn't be more wrong.
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Are Wrexham still favourites to finish in the top six? Of course not, particularly following their emphatic defeat to Southampton.
Opta's data model gives Parkinson's men just an 18.84% chance of ending the regular season in the top six, down by more than 20% compared to what it was during the recent international break.
But to say Wrexham are now out of the running to reach the play-offs would be as daft as it would be inaccurate.
Midfielder Matty James - who returned to action as a substitute against the Saints after two months on the sidelines with a toe injury - referenced when his side dropped out of the top two spots last season, prior to ultimately clinching automatic promotion from League One, in the post-match press conference.
This is a side that has dealt with setbacks time and time again in the Parkinson era.
They are also a team fully capable of springing a surprise or two, as they have shown with impressive wins over the likes of leaders Coventry City and promotion-hopefuls Ipswich Town already this season.
And while there is obvious frustration and disappointment with the loss to the Saints, Parkinson was measured enough to focus on the bigger picture when facing the media after the Southampton loss.
"This game can't define the season," he said.
"We've worked exceptionally hard to get in this position. We're in a very tough division as everybody knows.
"With five games to go, we've got to make sure we batten down the hatches as a group and come out with a response at the weekend."
The Championship is notorious for providing a stage for drama, and Wrexham are no strangers to creating their own headlines.
Put the two together, and it should ensure that all hope should not yet be lost, even if they are now considerable underdogs.
Five games . . . five more opportunities.
