Lee Croft put in a good cross from the right, but Ched Evans was denied a header by Sam Ricketts.
There was no denying Dion Dublin though. He timed his leap to perfection when Darel Russell crossed from the right and his looping header from 12 yards beat Boaz Myhill's despairing dive to his right.
Myhill then pulled off an acrobatic save to keep out a fierce shot from Croft after Gary Doherty had made a goalline clearance to deny Michael Turner.
From Hull's first corner, Ian Ashbee's shot went a yard wide.
In the 39th minute Wayne Brown out-jumped the Norwich defenders, but his header from Jay-Jay Okocha's right-wing free-kick cleared the bar.
David Marshall pulled off a fantastic one-handed save to keep out Fraizer Campbell's header from Simon Walton's right-wing cross, but a minute later Campbell's pace took him past two Norwich defenders and he rolled the ball under Marshall for the equaliser.
The Norwich keeper made another good save to deny Ryan France as the Tigers threatened to take the game by the scruff of the neck.
In the 67th minute Mark Fotheringham went close with a rasping shot which was only inches over the bar.
Fotheringham, Russell and Jason Shackell had shots blocked in a packed penalty area as Norwich put the Tigers under pressure in the last quarter of the game, but the visitors hung on for a hard-earned point with Campbell always looking dangerous on the break.