It was a draw which felt like a defeat.
Wednesday let slip a golden chance to send out a statement of promotion intent to the rest of the Championship.
Leading two nil at half-time after another stunning Adam Reach strike and poacher's finish from Fernando Forestieri, the Owls appeared on course to beat high-flying West Bromwich Albion and move into the play-off positions for the first time this season.
But their defensive frailties were once again exploited late on as the in-form Baggies scored twice in three minutes to leave them still searching for a first league clean sheet.
Buoyed after his wonder volley against Leeds, Reach had the first chance of note. The reigning player of the year surged forward from deep before drilling a right foot shot high into the Leppings Lane end.
Wednesday, without key midfielder Barry Bannan through suspension and defender Ash Baker due to a leg injury, enjoyed the better of the early stages but things kept breaking down in the final third.
Hosting one of the Championship promotion chasers for the second time in six days, the Owls showed no fear in the opening quarter at a subdued S6. Joey Pelupessy was busy in the middle of the park, Reach provided the energy and creativity and Forestieri looked lively in attack.
However, clear-cut chances were at a premium.
It took WBA, who sat top of the league after the weekend's results, a while to settle. Former Wednesday midfielder Chris Brunt, brought in for Gareth Barry, curled a free-kick over before Cameron Dawson produced a routine stop to keep out Craig Dawson's downward header.
At the other end, Fernando Forestieri forced Sam Johnstone into action. His low right effort was parried by Johnstone and gathered by the Baggies shot-stopper at the second attempt.
Dwight Gayle, part of WBA's deadly front duo, felt aggrieved when he was not awarded a penalty after tangling with Michael Hector in the area.
Moments later, Reach lashed in yet another goal of the season contender. He collected Josh Onomah's pass, weighed up his options and unleashed a rasping left foot piledriver which gave Johnstone absolutely no chance. His stunning strike took his goal tally to four for the campaign.
No wonder Reach milked the applause. It was a moment to savour and the £5m man celebrated with Liam Palmer, who knelt down and pretended to shine Reach's shoe.
Oozing confidence and class, Reach raced on to Forestieri's lovely through ball before blazing over from an acute angle.
Cameron Dawson received some criticism following his shaky performance last time out but the academy graduate pulled off a brilliant save to foil Tyrone Mears. His one handed stop was crucial as moments later Forestieri doubled Wednesday's advantage.
WBA failed to clear Matt Penney's dangerous delivery from the left and Forestieri calmly slotted home at the back post.
The Baggies, the leading scorers in the division with 25 goals scored in 10 matches heading into this clash, were at times being made to look distinctly average.
But Wednesday rode their luck on the stroke of half-time as Darren Moore's men almost reduced the deficit when Gayle rattled the crossbar with a ferocious shot inside the box.
WBA, playing against the Owls for the first time in eight years, made a strong start after the restart and had a goal rightly disallowed after a blatant foul by Craig Dawson on Cameron Dawson.
Forestieri wasted a glorious chance to bag a third after robbing Ahmed Hegazi inside the Baggies box but he fired wide with just the goalkeeper to beat.
Forestieri ran the WBA defence ragged throughout. After a short corner with the excellent Penney, he tested the reflexes of Johnstone as the hosts pressed for a third.
It was no surprise the visitors made a triple substitution just after the hour mark as they looked to salvage a result. WBA briefly threatened a response, with Barry shooting narrowly wide when well-placed.
But Wednesday continued to pose the Baggies defence problems and Nuhiu sliced wide after yet more good approach play by Forestieri.
Credit WBA for not giving up and Pelupessy turned into his own net in the 86th minute after a great cross by Brunt from the right.
Barnes completed the Baggies stirring comeback following a mesmerising solo goal by Harvey Barnes. The talented Leicester City forward glided past three to four challenges before steering a shot past Dawson. Pelupessy will be disappointed he did not bring Barnes down in the build-up to the equaliser.
Things could have got even worse for the Owls in added on time but Welsh international Hal Robson-Kanu blasted just off target after another free-flowing move.
Luhukay said Wednesday would learn more about their promotion prospects after a tough-looking run of fixtures, featuring Aston Villa, Leeds United, WBA and Bristol City. His players have acquitted themselves well during this period but, on this evidence, they remain a work in progress.
Owls: Dawson; Lees, Hector, Pudil; Palmer, Pelupessy, Onomah (Kirby 82), Reach, Penney; Forestieri, Nuhiu (Joao 78). Substitutes: Wildsmith, Thorniley, Preston, Shaw, Fletcher.
WBA: Johnstone; Dawson, Hegazi, Bartley; Mears (Barry 56), Brunt, Livermore, Gibbs; Barnes; Rodriguez (Robson-Kanu 65), Gayle (Hoolahan 65). Substitutes: Myhill, Adarabioyo, Field, Edwards.
Referee: Oliver Langford (West Midlands)
Star man: Fernando Forestieri