The first effort of the game came just three minutes in when Martyn Waghorn fired towards the bottom right-hand corner of the Norwich goal, but goalkeeper Angus Gunn got down low to palm the effort away.
In the fifth minute, Jonas Knudsen let rip with a powerful left-footed shot from the edge of the box towards goal and, although Gunn was well beaten by the ferocious effort, the woodwork came to the rescue.
The tempo of the game slowed down briefly following the frantic start but it soon picked up again as Waghorn sliced the ball over the bar with the outside of his left foot following a corner.
From then on both sides enjoyed numerous chances, with the best effort of the first half coming on 40 minutes courtesy of the Blues.
David McGoldrick was presented with a free header about six yards out from a Waghorn free kick, but the 29-year-old wasted the opportunity by clearing the bar with his effort.
Despite the attacking intent shown by both Ipswich and Norwich, neither side could break the deadlock by the half-time whistle.
The breakthrough finally came just before the hour when Yanic Wildschut and Marco Stiepermann combined to set up James Maddison, who had all the time and space to compose himself in the box and slot home beyond Bartosz Bialkowski.
Norwich successfully took the sting out of the game thereafter, with Ipswich being held at bay by the wall of yellow, though Waghorn fired just over the bar from the edge of the area in injury time.