Brian Wilson killed off Wednesday and twice cleared off the line to leave Brian Laws' side in deep trouble and still searching for their first point of the season.
The Sheffield side, who have now leaked 11 goals in their opening four games, had new signings Akpo Sodje and Etienne Esajas on the bench.
Wednesday were handed an early chance when midfielder Steve Watson battled his way into the area before slipping the ball to Marcus Tudgay, but he pulled his low shot wide from eight yards.
They were made to pay in the fifth minute when Lee Johnson picked out Lee Trundle.
His short pass found Wilson who drilled the ball into the left-hand corner from 16 yards beyond the reach of Rob Burch.
Wednesday hit back in emphatic fashion carving out three chances in quick succession.
Tudgay saw his far-post strike stopped by Adriano Basso, before Wilson cleared the striker's spectacular overhead kick off the line.
Centre-back Richard Wood rose to meet Glenn Whelan's corner to finish with a tricky downward header which was hacked away by a combination of Basso and Wilson.
Frank Simek was caught napping after giving the ball away as Ivan Sproule outpaced the full-back before drilling the ball into the side-netting from the tightest of angles.
Lee Bullen replaced centre back Richard Hinds and Dutchman Esajas was brought on in the 56th minute to inject some life into the Wednesday side.
Jermaine Johnson twice had shots before he was replaced by targetman Sodje - a £250,000 transfer deadline signing from Port Vale.
Wilson saved City again on 70 minutes hacking the ball off the line after Deon Burton had got a touch to a Wood header.
Esajas almost snatched a spectacular equaliser in the dying minutes but Basso conjured up a spectacular stop to keep out the Dutchman's stinging free-kick from 22 yards.