The Owls posted their first away win of the season on Saturday, with Gary Madine claiming his seventh goal in five games to settle a lively affair at Huish Park.
Wednesday opened the scoring through loan debutant David McGoldrick before Kieran Agard hit a quickfire brace - the first in controversial circumstances - to put the Glovers in front.
But the Owls hit back themselves with Julian Bennett coming off the bench to score his second goal of the season.
And Madine nodded the winner to extend his current purple patch and cement his place at the top of the League 1 goalscoring chart.
Gary Megson shuffled his pack, with Reda Johnson at left back, James O'Connor back in the engine room and an immediate debut for new recruit McGoldrick.
Wednesday started well, playing neat possession football, with Yeovil very much on the back foot during the early exchanges.
McGoldrick looked lively in the final third and was rewarded with his first goal for the club ten minutes in. Ben Marshall sent an accurate cross to the back post, where McGoldrick peeled from his marker to power home a close range header.
The Owls went on to resume control of the game - until the turning point of the half came on 25 minutes.
The referee stopped play to allow treatment for Paul Huntington with Wednesday in possession in their own half.
The game restarted with Luke Ayling returning the ball to the Owls with a looped volley upfield but Agard was in hot pursuit of Rob Jones and the outrushing Richard O'Donnell.
O'Donnell and Jones collided just outside the box, leaving the Glovers' forward to steal in and slot into an empty net.
Wednesday protestations lasted a full five minutes but the goal stood, and to compound matters, Jones left the field through injury.
Twelve minutes later, things went from bad to worse for the Owls. Alan O'Brien crossed into the danger zone from the left and Agard controlled neatly before drilling firmly past O'Donnell to edge Yeovil in front.
The game was turned on its head and the only sight of goal Wednesday had during the remainder of the first half was a Madine header that sailed over the crossbar just before the break.
The hosts began the second period brightly and ex-Owl Steve MacLean forced a fine save from O'Donnell a minute after the resumption.
The Owls responded with Johnson having a low shot cleared off the line by Edward Upson and Marshall brought a reflex save from Jed Steer.
But from the resulting corner, the visitors were level. Marshall's delivery was a good one and Bennett was on hand to glance home into the far corner.
The Glovers pushed on, though, and MacLean again tested O'Donnell before the Owls hit the winner on 73 minutes, with Marshall again the provider.
The wideman aimed a pinpoint free kick into the six-yard box and Madine nodded a well-placed header into the back of the net to secure a deserved three points.
Yeovil: Steer, Ayling, Jones, Huntington, Blizzard (N'Gala 19), Upson, MacLean, Edgar, Ehmer, O'Brien (Massey 61) Agard (Gibson 80)
Unused substitutes: Haynes-Brown, Belson
Owls: O'Donnell, Buxton, Batth, Jones (Bennett 30), R Johnson, Prutton, Semedo, O'Connor, Marshall (Palmer 80), Madine, McGoldrick (Sedgwick 76)
Unused substitutes: Jameson, Reynolds