Yeovil only had themselves to blame as poor marking resulted in all three of the visitors' goals coming from headers inside the six-yard box.
McGoldrick, signed on-loan from Nottingham Forest on Friday, got the first after 10 minutes when he reacted at the far post to nod in Gary Madine's right-wing cross.
The Glovers hit back with two goals before half-time, both from Kieran Agard. The equaliser after 28 minutes was controversial. Agard followed up to prod the ball into an empty net when Owls goalkeeper Richard O'Donnell and his skipper Rob Jones collided after Yeovil tried to give the ball back to them following a drop ball at the other end of the pitch.
There was no controversy about Agard's second 10 minutes later when he ran on to a headed pass from Ed Upson to finish coolly.
The second half belonged to Wednesday. They equalised after 52 minutes when no-one picked up substitute Julian Bennett, who glanced in a Ben Marshall corner. The Yeovil defence was also to blame in the 72nd minute when Madine was unmarked to head in Marshall's free-kick from the left.