The Tykes scraped past Bolton Wanderers 2-1 on aggregate to punch their ticket to the capital, while Darren Moore's side pulled off the comeback to end all comebacks in their elimination of Peterborough United.
Match preview
While the events that unfolded at Hillsborough understandably made all the headlines, Barnsley welcomed Bolton to Oakwell having gleaned a respectable 1-1 draw from the first leg of their semi-final tie, and Michael Duff's side certainly made their territorial advantage count.
Despite only boasting 33% possession over the course of the 90 minutes, a first-half Liam Kitching header was all that was required for the Tykes to seal a slender aggregate win and keep their hopes of an immediate return to the second tier alive, although they were forced to survive an Aaron Morley free kick from inside the area fizzing over the bar after Harry Isted had handled a backpass.
In fact, that success over the Trotters ended an unsightly four-game streak without a win or clean sheet for Barnsley, who took just one point from their last nine regular-season matches in League One but still comfortably finished fourth in the standings, but the Tykes will no doubt possess the underdogs tag heading into Monday's winner-takes-all tie.
Wembley is unsurprisingly not a regular haunt for the Barnsley faithful, who have witnessed their team lose three of their five games under the iconic arch - although one of their two wins came in the 2015-16 League One playoff final versus Millwall, one month after they had bested Oxford United in the EFL Trophy final.
If any fans at home had only just switched on the TV towards the end of Sheffield Wednesday's semi-final second leg with Peterborough, they might have assumed that the travelling Posh army had invaded the Hillsborough pitch at the final whistle, as the visitors travelled to Yorkshire with a seemingly unassailable 4-0 lead from the opening encounter.
However, Darren Moore's men proceeded to write a page of EFL history with an unbelievable comeback, forcing extra time through Michael Smith, Lee Gregory, Reece James and - in the eighth minute of second-half injury time - Liam Palmer, leaving the Hillsborough crowd in raptures and the Posh players with their heads in their hands.
Sheffield Wednesday's fightback briefly looked to have been in vain when Gregory headed into his own net, but Callum Paterson sealed an incredible 5-1 win on the night to take the semi-final to spot kicks, where a missed Dan Butler strike proved telling.
On the back of that magnificent evening - which saw the Owls become the first-ever team to reach an EFL playoff final after losing the first leg of a semi by at least four goals - Moore's men make the long trip south aiming to right the wrongs of the regular season, where an Easter plateau forced them to accept third place behind Plymouth Argyle and Ipswich Town.
That 4-0 reverse to Peterborough represents the sole defeat from the Owls' last six matches - with the other five all ending in victory - but Barnsley did the double over Sheffield Wednesday in the regular League One season, and a fifth straight Wembley game without a win for Moore's men would render their astonishing semi-final feats inconsequential.
Barnsley League One form:
W
L
D
L
D
W
Sheffield Wednesday League One form:
W
W
W
W
L
W
Team News
While perhaps tempting fate, Barnsley boss Duff recently confirmed that he should have a full squad of players available for Monday's final, and the majority of the Tykes' team should therefore pick itself.
Despite his inexplicable and very nearly costly error in the second leg against Bolton, Isted will retain possession of the gloves as ever, while Oakwell hero Kitching links arms with captain Mads Andersen and Bobby Thomas in the back three.
James Norwood found the back of the net 11 times in the regular season, but the 32-year-old will accept another cameo role as Devante Cole and Manchester City loanee Slobodan Tedic join forces in attack.
Unlike Barnsley, Sheffield Wednesday have been sweating over the fitness of a couple of key players, with Marvin Johnson and Dominic Iorfa both looking a little worse for wear after the second leg versus Peterborough.
However, Moore has revealed that the pair have been in training as normal this week and will be fine for the trip to Wembley, and there is even a small chance that George Byers (hamstring) could play for the first time since March, having initially claimed that he would not be available for the rest of the season.
A spot on the bench awaits Byers if he is given the green light, though, as Moore also sticks with the same formula from their unparalleled second-leg success.
Barnsley possible starting lineup:
Isted; Thomas, Kitching, Andersen; Williams, Kane, Phillips, Connell, Cadden; Cole, Tedic
Sheffield Wednesday possible starting lineup:
Dawson; James, Ihiekwe, Iorfa; Patterson, Bannan, Palmer, Johnson; Windass; Gregory, Smith
We say: Barnsley 1-3 Sheffield Wednesday
With no second leg on offer to save their bacon, Sheffield Wednesday can ill-afford another disastrous display like their first-leg demolition at the hands of Peterborough, but Moore's side should live up to their favourites tag against a wholly inconsistent Barnsley outfit.
The Tykes should still make the net ripple at least once as their Yorkshire counterparts commit men forward, but having already scored a whopping 104 goals this season, the Owls can flaunt their attacking excellence to end their brief absence from the Championship.