ALBION were controversially denied a richly-deserved fourth successive victory when former Baggie Steve Watson netted a deflected last-gasp equaliser.
Kevin Phillips crowned his 50th Albion start by heading Tony Mowbray's men into the lead 14 minutes from time.
But the Owls preserved their near 33-year unbeaten record on Baggies soil in the most debatable of circumstances.
Despite the fourth official signaling only three minutes of stoppage time, referee Nigel Miller allowed play to continue into the 96th minute.
He then failed to spot a clear foul by Marcus Tudgay on Carl Hoefkens and Watson swept the loose ball past Dean Kiely.
The hosts had earlier had a 'goal' disallowed, hit the woodwork and were denied time and again by Wednesday keeper Lee Grant's brilliance.
But their pressure finally paid off when Phillips broke the deadlock by scoring for the third successive game - his tenth of the season.
The game, however, ended on a sour note for talisman Phillips when he was stretchered off nine minutes from time.
The hosts, who had already used all their subs, soldiered on with ten men - until Watson struck a cruel leveller.
After Saturday's stunning 3-0 win at league leaders Watford, Mowbray made one change, replacing James Morrison with Filipe Teixeira.
Albion started the day in third spot, one point behind second-placed Bristol City, as they prepared to entertain Brian Laws' 18th-placed team.
The game got off to a sluggish start which wasn't helped by a lengthy injury delay after Ishmael Miller and Akpo Sodje clashed heads inside the Owls box as they competed for a Martin Albrechtsen cross.
Sodje was able to continue while Miller disappeared down the tunnel for further treatment.
The Baggies may temporarily have been down to ten men, but that didn't stop them pummeling the Owls box with a succession of crosses.
Miller finally reentered the fray with his head bandaged - some five minutes after his bang to the head.
And the on-loan Manchester City marksman soon showed he was thinking clearly by recording the first shot on goal, teasing his way past Mark Beevers before seeing a 20-yard grass-cutter well held by Lee Grant.
Albion looked in complete control as they confidently stroked the ball around the park - until Saturday's man-of-the-match Zoltan Gera dangerously gifted Tudgay the ball inside the Albion half.
It took a vital Albrechtsen block to prevent the Owls striker troubling Kiely and then Bostjan Cesar had to make an acrobatic headed clearance over his own bar from Jermaine Johnson's cross to snuff out the danger.
But there was another nervous moment from Burton O'Brien's subsequent corner, with giant centre-half Beevers heading just over.
Albion thought they'd broken the deadlock in the 20th minute when Miller raced onto Teixeira's clever throughball and saw his low cross turned into his own net by Wednesday right-back Frank Simek.
But the effort was ruled out for offside.
Albion now had real momentum and a terrific one-two between Paul Robinson and Teixeira set up an awkward chance for Gera, who volleyed over from 15 yards.
Teixeira was becoming increasingly influential and it took a vital last-ditch challenge from Beevers to prevent Miller stabbing home the ex-PSV maestro's low centre.
Teixeira then exchanged a quick give-and-go with Phillips before placing a 20-yard effort over the bar.
Wednesday had barely got out of their own half for some time but went close in the 37th minute when Tudgay flashed a downward header just wide from Johnson's dangerous free-kick.
Back came Albion and Grant had to pull off a flying one-handed save to keep out Miller's 20-yard cracker following great work by Phillips.
The Baggies went even closer from Jonathan Greening's flag-kick, which fell invitingly for Phillips.
The ex-England man swiveled on the edge of the six-yard box and fired against the far post before the Owls scrambled the ball out for another corner.
Mowbray had to make an early change in the 40th minute, replacing the injured Albrechtsen with Pele.
Wednesday threatened again when Sodje battled his way into the box and Hoefkens had to make a vital block to keep out Tudgay's 12-yard snapshot.
Albion created a glorious opening within three minutes of the second-half kicking off.
Robert Koren's sublime slide-rule pass sent Hoefkens racing away down the right and the Belgian star pulled the ball back to Phillips 20 yards out.
The 34-year-old hitman took a touch before lashing a left-footed shot just over.
Another chance went begging moments later when Koren left Owls left-back Tommy Spurr for dead.
The Slovenian teed up Miller eight yards out but the 6ft 3in striker failed to even trouble the goal with a swing of his weaker right foot.
Wednesday couldn't get out of their own half again and the Baggies pressure continued when Miller held off two defenders and saw his ferocious near-post drive blocked by Grant's legs.
The visitors didn't threaten again until the hour mark when Simek fired well wide from 25 yards.
Wednesday had another let off when Miller inadvertently got in the way of Teixeira's goalbound shot from just inside the box, taking the sting out of it and giving Grant an easier save.
Albion really had the bit between their teeth and Grant had to pull off a fine save to keep out Phillips' acute shot from Greening's neat ball into the box.
And the Owls No.1 even bettered that stop by somehow getting down to his left to claw away Robinson's downward header from Koren's exquisite diagonal ball.
Albion kept knocking on the door and Grant did well to clutch Phillips' low 20-yard drive in the 71st minute.
Phillips had his head in his hands again three minutes later when he whipped a right-footed shot from a similar distance - which appeared to beat Grant all ends up - inches past the far post.
But the breakthrough finally came 14 minutes from time - fittingly from Phillips.
Robinson found the ex-Sunderland marksman with an inch-perfect left-wing cross and Phillips headed low inside Grant's left-hand post.
However, that proved Phillips' last contribution as he was stretchered off in the 81st minute, leaving Albion to play out the dying stages with ten men as Mowbray had used all his subs.
Despite being a man down, Albion did not look in any danger until the sixth minute of stoppage time.
Hoefkens was clearly clattered by Tudgay as he shaped to head the ball out of the box.
But referee Miller allowed play to continue and the rebound fell to Watson who saw his deflected low drive beat Kiely.
ALBION (4-4-2): Kiely; Hoefkens, Albrechtsen (Pele 40), Cesar, Robinson; Teixeira (Morrison 64), Greening, Koren, Gera (Brunt 75); Phillips, Miller. Subs not used: Bednar, MacDonald.
SHEFF WED (4-4-2): Grant; Simek, Hinds, Beevers, Spurr; J Johnson (Small 68), Whelan, Watson, O'Brien (Burton 73); Sodje (Esajas 87), Tudgay. Subs not used: Folly, Bullen.
GOALS: ALBION - Phillips (76). SHEFF WED - Watson (90+6).
BOOKINGS: ALBION - Cesar (foul 23).
REFEREE: N Miller (Durham).
ATTENDANCE: 19,807.
ALBION STARMAN: Robert Koren.
PIC: KING KEV...Phillips heads Albion ahead
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