Referee Mick Russell denied Norwich two penalties and then ruled out what appeared to be a perfectly good headed goal by David Mooney for an alleged foul.
The home side kicked off attacking the River End goal but it was the visitors who created the early pressure after forcing two corners inside the first five minutes.
David Marshall then saved a low angled drive from Marcus Tudgay.
In the 12th minute, Jon Otsemobor made a determined run into the penalty area but his low cross was cleared by the well organised Wednesday defence.
Mooney latched onto a weak back header but his shot hit the side-netting.
Alan Gow put in a low cross from the left but Mooney failed to make a clean contact with the ball.
Norwich were denied a penalty when Mr Russell missed a handball by Richard Wood.
At the other end, Marshall did well to save Tudgay's shot and Darren Potter went close with a fierce rising drive from long range.
Lee Grant kept out Jason Shackell's header from a Simon Lappin corner ensuring the first half ended goalless.
However inside the third minute of the second half, Jermaine Johnson beat Lee Croft in the City right-back position and his angled shot from 18 yards took a wicked deflection off Otsemobor and beat Marshall at his near post.
Gow was tripped by Sean McAllister but once again Mr Russell ignored penalty appeals.
Alan Lee replaced Croft after 68 minutes and unsettled the Wednesday defence.
Gow went close with a rising drive and five minutes from time, Mooney's header crossed the line but Mr Russell angered City players and fans alike by awarding a free-kick for no obvious reason.