Robert Earnshaw's opportunist strike put the Canaries ahead in the 72nd minute, but they allowed the Tigers to roar back and Michael Turner arrived in the right place at the right time to net a hard-earned point for the visitors in stoppage time.
The home side kicked off attacking the River End goal and, in the seventh minute, Hull keeper Boaz Myhill had to be at full stretch to turn away Darren Huckerby's volley from the first corner of the game. A minute later Nicky Forster's shot was deflected for a corner.
With a quarter-of-an-hour played Paul Gallacher required treatment after a collision with Forster.
Damien Delaney went close with a header from Dean Marney's free-kick and Gallacher did well to keep out a fierce shot from Forster.
In the 43rd minute Robert Eagle crossed from the left but Earnshaw failed to make a clean contact as the ball bobbled in front of him.
In first-half stoppage time Paul McVeigh's shot was blocked and Craig Fagan's effort grazed the outside of a post.
The home side started the second half looking more purposeful and Peter Thorne replaced Eagle 12 minutes after the break.
In the 72nd minute Thorne headed the ball back to McVeigh and his forward header was touched past Myhill by Earnshaw's right boot from six yards out.
It was McVeigh's last contribution in the game before he was substituted by Andrew Hughes.
With ten minutes to play Earnshaw got his head to Huckerby's left-wing cross but his looping header landed on top of the net while at the other end Stuart Elliott's shot shaved a post.
Hull snatched an equaliser deep in stoppage time when Norwich failed to clear Elliott's deep cross from the left.
The ball was then headed back across goal, first by substitute Ryan France and then by the other sub, Nicky Barmby, and Elliott finished the move with a right-foot volley from eight yards out that gave Gallacher no chance.