They failed to build on an early goal from Iain Hume and then allowed Wednesday to regroup and register their first win in nine attempts in front of the Championship's highest attendance of the season.
City threatened after two minutes when a Jamie Clapham free-kick triggered an almighty scramble inside the Wednesday penalty area with Steve Howard's goalbound shot blocked, followed by a Gareth McAuley effort, which was turned away for a corner, which the visitors were grateful to clear.
Any nerves Leicester might have had were soothed on nine minutes with a goal from top-scorer Hume.
A long clearance by Paul Henderson appeared to carry no threat, but when Lee Bullen's weak back-header failed to reach his keeper, Hume took full advantage to control the loose ball and guide it calmly into an unguarded net.
The Foxes suffered a blow on 20 minutes when defensive lynchpin Patrick Kisnorbo was stretchered off after landing awkwardly while repelling an aerial raid from Wednesday.
Leicester retorted with a breakaway and a James Wesolowski shot, which had Lee Grant at full stretch.
The Owls were thrown a lifeline after 28 minutes when they were awarded a penalty after Barry Hayles handled a Franck Songo'o corner at the back post.
Deon Burton struck the spot-kick well enough but Henderson guessed correctly, diving to his left to make the save.
Howard then shot wide for relieved City before Hume's penalty claims after a clumsy challenge by Mark Beevers were waved aside.
City were made to rue their missed chances when Wednesday equalised moments before the break when, with McAuley out of position, Bartosz Slusarski held the ball up before turning David Bell and shooting home from 14 yards.
Leicester appeared drained of confidence by Wednesday's leveller and it was no surprise when they fell behind on 53 minutes when the home rearguard failed to cut out a low cross from Songo'o, with unchallenged Steve Watson having the time and space to steer the ball home from ten yards.
Shaken City struggled to regroup but went close on the hour mark when McAuley's downward header drew a reflex save from Grant.
Then it was Leicester's turn to be thrown a penalty lifeline on 66 minutes when Wednesday substitute Jermaine Johnson handled inside the box.
The odds were on City's most prolific scorer finding the net again, but instead Hume blasted the spot-kick wide of the goal.
Grant then exhibited fine reactions to keep out Bruno N'Gotty's downward header as City fought hard for an equaliser.
Their final chance came when Howard shot wide after he was put through by Bell.
It was all over for Leicester on 90 minutes when a long clearance found substitute Leon Clarke unmarked and, with Henderson charging off his line, Clarke kept a clear head to lob the ball into the net from 25 yards.