For an hour it looked as if they would not turn possession into goals, but then Lee Croft hit a screamer and eight minutes from time Matty Pattison made sure of the points when he blasted home from close range.
The home side kicked off attacking the River End goal and, after five minutes, Jon Otsemobor fired in a shot which landed on the roof of the net.
The next threat to the Ipswich goal came from Leroy Lita when his header from David Bell's corner was turned over by Richard Wright.
Norwich did most of the attacking with Croft causing problems for his marker David Wright.
It was half-an-hour before Ipswich threatened the Norwich goal when Owen Garvan's corner was headed over by Alex Bruce.
At the other end, Sammy Clingan's goalbound shot took a deflection and hit the top of the bar, but referee Lee Probert angered the home fans by giving a goal kick.
In the 45th minute Lita's deft touch put Pattison through, but his shot went straight at Richard Wright.
Ipswich started the second half on the front foot and David Marshall did well to keep out a shot from Jon Walters in a one-on-one situation.
City weathered Town's pressure and, in the 57th minute, Lita set up Wes Hoolahan, but his shot went inches over the bar.
On the hour Croft collected the ball from Pattison and let fly from some 25 yards with a superb right-foot shot which beat Wright high to his left. Lita then fired into the side-netting after being released by Croft.
Ipswich substitute, Danny Haynes, had a header saved by Marshall as the visitors began to enjoy a fair share of the possession.
However, when Bell drifted in a well-flighted free-kick from the left wing, Gary Doherty got his head to the ball at the far post and it fell kindly for Pattison whose right-foot shot hit the back of the net with considerable force.