The City forward line rarely threatened and for most of the second half the visitors had the upper hand in midfield.
There were several warnings for the home defenders before Wade Small wrapped up the points with a simple goal from Frankie Simek's well placed pass.
The Canaries kicked off attacking the Barclay End goal but were on the defensive for the first five minutes.
Francis Jeffers headed wide from Simek's right-wing cross and Gary Doherty did the same at the other end from Simon Lappin's right-wing free kick.
Michael Johnson did well to cut out Darren Huckerby's left-wing cross, then Johnson was caught by Michael Spillane, rolling over dramatically thereby ensuring the City youngster got a yellow card.
Graham Kavanagh was booked after checking Huckerby's stride before the injured Jeffers made way for Marcus Tudgay.
Steve Watson produced the first real shot on target three minutes into the second half but it went straight at David Marshall.
At the other end, Lee Grant could only palm away Jamie Cureton's shot, but the City striker could only find the stand when he hit the rebound over the bar.
Watson limped off and was replaced by Jermaine Johnson.
On the hour the Wednesday keeper did well to pounce on the ball when Spillane was about to get a boot on Chris Brown's neat back heel.
Spillane made way for Lee Croft on 62 minutes, then Glenn Whelan was booked for pulling back Huckerby.
A couple of promising Wednesday moves ended with wayward shots with the visitors creating the best chances.
In response to this, David Strihavka was sent on for Brown, but on 76 minutes Small was left unmarked at the far post and converted Simek's low cross from the right with a crisp right-foot shot from seven yards which went under Marshall's dive to his right.
From then on the home side never looked like getting anything from the game and the final whistle produced cries of "what a load of rubbish" from a large section of the home fans.