The Owls were hit with a late hammerblow by high-flying Millwall following a tense finish at Hillsborough.
Stuart Gray’s side looked for a second win in three matches so far after Chris Maguire’s deflected free kick gave them the lead and Millwall went on to miss a penalty.
But deep into five minutes of added time disaster struck for the hosts when Magaye Gueye drilled high into the net from 15 yards as the Owls scrambled to defend.
There was little between the two sides for much of the contest but it appeared as though the Owls had done enough to cling on.
It was the defences who were on top in a tame first half but each side had the chance to take the lead.
Lee Martin went closest for the Lions during the early stages as he pulled a free kick just wide.
But Atdhe Nuhiu could easily have put the Owls in front when he met a Chris Maguire corner but powered his header over the bar.
A Tom Lees header drew a save from David Forde from another corner moments later.
Martyn Woolford really ought to have put Millwall ahead late in the half but fired well over from a great position.
And it took a fine save from Keiren Westwood at the feet of Lee Gregory to keep the visitors out again.
The Owls had a penalty shout in the dying stages of the half when Jacques Maghoma was tumbled in the box but referee Nigel Miller waved play on.
A heavily deflected Chris Maguire free kick saw the Owls break the deadlock against fellow unbeaten side Millwall on 57 minutes.
Maguire fired a free kick on goal from the right but the ball took a wicked deflection off the wall and flew past a stranded David Forde.
After Maguire gave the Owls the lead, Woolford almost drew Millwall level when his shot from distance flew inches over the bar.
Maguire fired over the bar himself with a fierce effort as Wednesday looked to stretch their advantage.
Millwall missed a penalty as the Owls clung onto their lead by their fingernails.
Referee Nigel Miller pointed to the spot after Keiren Westwood was adjudged to have brought down Lee Martin.
Shaun Williams stepped up and cannoned his spot kick back off the post to see Wednesday stay in front.
The visitors pushed hard for the leveller following their missed penalty and Scott Malone volleyed over from a great position.
Just when it seemed as though luck would shine on the Owls, the ball was laid off to Gueye and he rifled past Westwood to secure a share of the spoils and see both sides remain unbeaten.
Owls: Westwood, Palmer, Loovens, Lees, Mattock, Maguire, Hutchinson, Semedo, Maghoma, Nuhiu, May.
Subs: Kirkland, Zayatte, Coke, McCabe, Helan, Corry, Madine.
Millwall: Forde, Edwards, Dunne, Beevers, Malone, Williams, Abdou, Martin, Woolford, McDonald, Gregory.
Subs: Gerrar, Wright, Easter, Briggs, Webster, Gueye, Fuller.
Referee: Nigel Miller.