Dickson Etuhu gave City a dream start with a near-post header from Darren Huckerby's left-wing cross after just five minutes.
However, the Canaries failed to press home the advantage and Ipswich started the second half looking the better side. It was no great surprise when David Wright equalised after some scrappy defending inside the City six-yard box.
The home side finished the stronger but in the end had to settle for a draw which leaves Town above City in the Championship table.
Norwich kicked off attacking the Barclay End goal and Shane Supple was soon in action cutting out a Huckerby left-wing cross before it reached Robert Earnshaw.
However, in the fifth minute Etuhu met an identical Huckerby cross with a firm near-post header, beating Supple from five yards out.
In the 12th minute Etuhu got his head to Mark Fotheringham's right-wing corner, but this time the ball went wide of the near post.
Huckerby's shot cleared the bar after 17 minutes and Etuhu's long-range effort also found the fans behind the goal.
Supple did well to hold on to Huckerby's low shot then Earnshaw had his first shot of the match after 33 minutes, but it was too high.
Francis Jeffers brought a save from Tony Warner four minutes from the break and Earnshaw was unlucky to be wrongly flagged offside.
Gavin Williams had a shot saved by Warner six minutes into the second half. Five minutes later Chris Martin replaced Michael Spillane. He almost made an immediate impact, but his far-post volley from Huckerby's left-wing cross went inches over the bar.
Within seconds Ipswich were level, Wright scoring with an angled drive after his low cross from the right had been blocked inside the six-yard box.
Jon Walters then made way for Alan Lee and Lee Croft limped off to be replaced by Jurgen Colin.
Williams saw his fierce drive turned for corner by Warner. In the 75th minute birthday boy Dion Dublin was only inches away from getting his head to a Huckerby cross.
The Town talisman, Danny Haynes, replaced Jaime Peters 12 minutes from time. Supple blocked Huckerby's deflected shot with his legs and Earnshaw tried to turn in Huckerby's left-wing cross, but failed to find the target.
As the home side regained the initiative Fotheringham fired over with a long-range free-kick and Etuhu headed wide.