The Owls suffered a 2-1 defeat against Bury on Tuesday evening at Gigg Lane.
First half goals from skipper Ryan Lowe and Damien Mozika sealed the points for the Shakers.
Wednesday hit back after the break with Chris Sedgwick striking superbly into the top corner minutes after the restart, but Bury were able to hold on for their first league&nbsp;win of the new campaign.
Wednesday made a bright start and dominated the early possession as David Prutton saw his early strike deflected wide for a corner.
Danny Batth came close from the resulting flag kick but couldn't get the necessary purchase from Chris Lines' delivery.
But despite the Owls' early impetus, it was Bury who struck first after seven minutes.
David Worrall's whipped ball into the box from the right picked out Lowe who steered his header into the top corner.
A deep cross from Lewis Buxton gave Julian Bennett a sight of goal at the back stick but the defender's header flew wide of the target.
Sedgwick then went close with a powerful drive from 25 yards that just cleared the crossbar before Andy Bishop should have done better at the other end with his header wide from five yards.
A free kick from deep by Bennett picked out the towering figure of Reda Johnson, whose downward header was cleared over the bar.
Wednesday were beginning to up the ante in the final third as Lines fed an advancing Buxton who shot low across goal but the wrong side of the upright.
Things got worse for Wednesday five minutes before the break when Mozika powered his way through on goal and calmly sidefooted past Richard O'Donnell.
The Owls had the ball in the net two minutes later through Johnson but the goal was ruled out for the defender's challenge on Bury keeper Cameron Belford.
A rejuvenated Wednesday side came out after the break and within minutes of the restart, Gary Megson's men had the ball in the net.
Following a quick burst upfield from Prutton, the midfielder played the ball to Sedgwick on the left who cut inside and curled a delightful shot into the far corner off the underside of the crossbar.
Wednesday were visibly lifted by the goal and had another ruled out moments later. Otsemobor's low ball across the face of goal was prodded home by Gary Madine but the flag was up for offside.
The early goal had set up an action-packed second period at Gigg Lane as Mozika went inches from regaining Bury's two-goal advantage with an arrowing drive from distance that flew wide of O'Donnell's right hand post.
Danny Uchechi was thrown into the attack with ten minutes remaining as the Owls went in search of a late equaliser.
Lowe went close again at the death but his low strike was well kept out by O'Donnell as the referee brought an end to the action, with Bury holding on to their slim lead.
Bury: Belford, Picken, Skarz, Sweeney, Worrall (Cregg 90), Bishop (John-Lewis 89), Jones, Lowe, Sodje, Hughes, Mozika
Unused substitutes: Futcher, Branagan, Oyenuga
Owls: O'Donnell, Buxton, Batth, R Jones (Johnson 14), Bennett, Semedo, Prutton (Uchechi 79), Lines, Sedgwick, O'Grady (Otsemobor 29), Madine
Unused substitutes: Cuff, Morrison