Jonas Knudsen’s goal on half-time gave Town a share of the local spoils at Portman Road.
The Danish international found the net with a right foot drive from the edge of the box to cancel out Cameron Jerome’s opener midway through the half.
Teddy Bishop went close to a winner late on while Steven Whittaker hit the inside of the post for Norwich in an entertaining 90 minutes.
Town started really brightly and Jonathan Douglas had the ball in the net inside the first minute after Daryl Murphy headed on but the offside flag was raised to cut Blues’ celebrations.
Murphy then went close with a right foot effort from inside the box as Town pressed the Canaries back.
Grant Ward got around the back but his cross was cleared, then Jerome threatened at the other end but couldn’t poke the ball past Bart Bialkowski.
Murphy’s strength was troubling the visitors and he forced his way past Timm Klose before going down in the box but referee David Coote waved away any penalty appeals.
Wes Hoolahan saw his shot blocked by a terrific challenge from Christophe Berra, Murphy’s header landing on the roof of the net from Ward’s excellent cross as Town edged the openings.
Knudsen’s cross was headed back across goal by Luke Chambers but Ward couldn’t find the space to get a shot in, Murphy’s header comfortably saved by Michael McGovern, his counterpart Bialkowski quickly off his line to deny Jerome.
It was the Canaries who went ahead though on 25 minutes, Jerome sliding the ball home after Jonathan Howson had found him inside the box, following a burst down the right by Ivo Pinto.
Naismith fired over after another run and cross by Pinto, then Knudsen almost got on the end of Ward’s cross as Town looked for the equaliser and it was the Dane who provided it with a right foot strike on the stroke of half-time.
Knudsen and Ward sent in testing crosses as the second-half got underway, Berra seeing a goalbound header from a corner cannon to safety then Adam Webster was in the right place to clear off the line from substitute Whittaker’s shot.
Murphy almost got in on goal but Klose’s outstretched foot just did enough to divert the ball back to McGovern.
Kevin Bru’s 25 yard free-kick was smothered by the Norwich wall, before Town made a first change with Teddy Bishop on for Bru for the last 20 minutes.
Knudsen did well to stop substitute Jacob Murphy’s cross finding Jerome, Sears’ shot catapulted to safety before Town had a slice of luck when Whittaker’s shot cannoned back off the inside of the post.
Bishop almost won it for Blues when he robbed Whittaker inside the box but he couldn’t beat McGovern before Sears made way for Luke Varney for the final few minutes.
Jacob Murphy and Hoolahan went close for the Canaries in added on time but Town held firm for a deserved point at the least.
TOWN: Bialkowski, Chambers, Webster, Berra, Knudsen, Skuse, Douglas, Bru (Bishop 70), Ward, Sears (Varney 88), Murphy. Subs not used: Gerken, Smith, Kenlock, Dozzell, Pitman.
NORWICH: McGovern, Pinto (Whittaker 46), Klose, Bennett, Brady, Mulumbu (60), Howson, Hoolahan, Tettey, Naismith (Canos 79), Jerome. Subs not used: Jones, Bassong, Martin, Lafferty. Booked: Tettey.