Both sides hit the woodwork in a game that Ipswich deserved to win. The City defence always looked uncomfortable in dealing with the physical presence of Alan Lee and the pace of young Danny Haynes.
The Norwich forwards fell too easily into Ipswich's offside trap.
The home side kicked off attacking the Barclay End goal but the visitors enjoyed the best of the early exchanges, forcing three corners in the first eight minutes before Darren Currie brought a smart save from Robert Green with a well-struck long-range shot.
Norwich replied with a free-kick from Youssef Safri that was deflected for a corner.
Fabian Wilnis came close to scoring an own goal when forced to head over the bar to clear a cross from Andrew Hughes.
New boy Robert Earnshaw was twice caught offside before Currie forced Green to make a fingertip save midway through the first half.
Town brought on Haynes for Gavin Williams after just 25 minutes.
Jonatan Johansson forced Lewis Price to tip his fierce shot over the bar while, at the other end, a Matthew Richards shot came back off a post.
Norwich finally sprang the offside trap in the 33rd minute when Johansson timed his run to perfection as he picked up Safri's throughball and finished with a right-foot lob over Price from the edge of the penalty area.
Ipswich were level five minutes later when Jimmy Juan's 25-yard free-kick found the inside of Green's right-hand post after taking a wicked deflection off City's defensive wall.
Norwich should have regained the lead in the dying seconds of the first half but Zesh Rehman fired over from close range.
Norwich made a double substitution at half-time, Dickson Etuhu making way for Carl Robinson and Darren Huckerby replacing Hughes.
Lee's header went straight to Green but the City keeper had more to do when Richards fired in another fierce drive on 65 minutes.
Owen Garvan was lucky to escape with a yellow card for a reckless challenge on Earnshaw and Johnasson hit a post when the resulting free-kick was flicked on by Paul McVeigh.
The winning goal came after 88 minutes when Richards crossed from the left. Lee headed the ball back across the goal and Haynes bundled the ball inside Green's right-hand post with Gary Doherty trying desperately to clear off the line.