The Owls looked comfortable after a controversial Atdhe Nuhiu strike put them ahead after 25 minutes, and more so when Yeovil had Byron Webster sent off three minutes before half-time.
But the home side's lead was cancelled out by a terrific Joe Ralls finish after 64 minutes that leaves both sides in early trouble at the wrong end of the table.
After a scrappy start it was Wednesday who crafted the first opportunity, when a cross from Jordan Spence was met by Nuhiu. His header was easily saved by on-loan goalkeeper Wayne Hennessey.
Yeovil responded a minute later as a pass through the middle of the home defence was met by James Hayter who placed his shot to the side of Chris Kirkland. Kirkland got a finger to it, slowing the ball so it could be cleared off the line.
Wednesday then opened the scoring through Nuhui. The Austrian was offside from the initial ball but left it to an onrushing Michail Antonio. The Yeovil defence watched Antonio send it across the goal to Nuhui for an easy tap-in.
The decision left both the defence and linesman confused. The touchline official had raised his flag for the initial offside but after heated discussions referee Geoff Eltringham allowed the goal to stand.
It inspired the Glovers and they almost scored two minutes later as only a high-quality save from Kirkland prevented Andy Williams' header from levelling the scores.
The job was made harder for Yeovil as Webster was given his marching orders after a tussle with Nuhui left them both on the ground and Webster seemed to strike out at the Owls forward.
Despite being down to 10 men, Yeovil could have gone in at half-time on level terms as a curling Ed Upson free-kick was saved brilliantly to his left by Kirkland.
The Owls started positively in the second half, with Nuhui hitting a shot over the bar early on, but Yeovil managed to draw themselves level.
A ball from a deep free-kick eventually landed at the feet of Ralls, who put the ball on to his left foot and drove his shot across Kirkland.
Yeovil goalkeeper Hennessey almost gifted Wednesday a winner as a volley from Antonio after 73 minutes nearly squeezed its way through, but the Wales international managed to recover and stop the ball crossing the line.
There was little threat after that from Wednesday and the result leaves both sides with four points after six games.