They should be there by right, rather than awaiting a replay after giving the Canaries the runaround for long periods.
City relied heavily on the skills of Darren Huckerby and Youssef Safri -without them they would have looked rather insipid.
They had to thank goalkeeper David Marshall - on loan from Celtic - for a magnificent save in the fourth minute of stoppage time that earned them a second chance when he clawed away a goal-bound header from Blackpool's Latvian defender Kaspars Gorkss.
City were down to ten men at this stage with Chris Brown earning his marching orders for a silly display of dissent with eight minutes to go.
Blackpool had started brightly with Andy Morrell guiding a header just wide and Keith Southern forcing an early save from Marshall.
The keeper then had to produce a fine block with his legs after David Fox had cleverly played in Scott Vernon whose angled drive was blocked at the near post by Marshall.
After 20 minutes Blackpool had a strong penalty shout turned down when Gary Doherty appeared to man-handle Morrell in the box. But, as the Seasiders appealed in vain, City counter-attacked and Huckerby sent a cross tantalisingly across the face of goal.
Huckerby continued to prove a handful and good work by the winger allowed Carl Robinson to have an 18-yard shot on goal, which was brilliantly clawed away by Rhys Evans. A minute later - the 25th - Huckerby produced another cross-cum-shot but he had no support.
With Wes Hoolahan producing some brilliant midfield touches, Blackpool continued to press but, just before the break, they ruined all their good work.
Former Canary Adrian Forbes had a pass closed down in his own half in the third minute of stoppage time - the fourth official had signalled just two minutes. The ball ricocheted across the Blackpool penalty area and fell into the path of Huckerby, who cut inside and scored with an excellent low drive.
In a fine advertisement for Cup football the game moved from end to end in the second half and Blackpool equalised in the 51st minute. Fox's lovely free-kick found Ian Evatt, who crashed a far post header past Marshall.
City had their best second-half chance in the 62nd minute, when they counter-attacked after a mistake in midfield by Southern. Brown was left with a one-on-one with keeper Evans, but Blackpool's last line of defence came out bravely to block at Brown's feet.
City then survived some torrid moments and another strong penalty appeal as Blackpool brought on substitutes Keigan Parker and Ben Burgess in a desperate attempt to break the deadlock. Both had fine chances, but found Marshall in dominant form.