While the Sheffield side had most of the possession, last season's beaten play-off finalists carved out the clearer chances, record signing Nicky Maynard missing the best opening of the game.
City, with just one win from ten games, almost found a way through in the opening minutes, Michael McIndoe threading the ball to Ivan Sproule who was foiled by a last-ditch Tommy Spurr tackle.
The Hillsborough side, decimated by injuries and with 17-year-old academy player Nathan Modest on the bench, hit back on 15 minutes.
Francis Jeffers picked out Leon Clarke as the big striker, surrounded by three players, surged into the box to finish with a stinging left-foot strike, which was palmed away by the acrobatic Adriano Basso.
Clarke almost broke the deadlock minutes before the break when centre-back Liam Fontaine blundered as he headed back to his keeper. Basso was forced to sprint off his line to block Clarke's shot ten yards from goal.
City should have snatched the lead seconds after the re-start, Sproule setting up Maynard who raced through unmarked before firing wide from 12 yards.
Marvin Elliott had Wednesday keeper Lee Grant scrambling back with a cross-cum-shot, the ball dropping the wrong side of the bar.
Wednesday were in trouble again as City gained the upper-hand. Substitute Lee Johnson's deep cross was headed back by Jamie McCombe with Stern John just failing to add the finishing touch at the far post.
Mark Beevers foiled Maynard with a perfectly-timed tackle in the area with the Wednesday defence again exposed.
Marcus Tudgay, his head bandaged from a first-half injury, pulled his diving header wide and had another shot deflected away from danger as the Sheffield side looked for a winner.