Teenage striker Chris Martin came off the bench to grab his first Norwich goal and settle a pulsating FA Cup tie.
Two-goal hero Huckerby (left) was lucky to be on the pitch to see Norwich through
Michael Jackson headed Blackpool ahead but Darren Huckerby, who was lucky to be on the pitch after a nasty tackle on Paul Tierney, levelled in normal time.
Huckerby scored a second superb curling effort five minutes into extra-time.
Shaun Barker's tap-in seemed to have forced penalties but Martin shot home to book a glamour fifth round tie against Chelsea at Stamford Bridge.
But the visitors will be rueing the fact they failed to wrap up the game long before Wesley Hoolahan's terrible defensive header allowed Martin to score past Rhys Evans.
The lively Keigan Parker squandered a hat-trick of chances to extend their first-half lead in normal time.
Parker saw an early shot go narrowly wide and former Norwich winger Adrian Forbes had a speculative effort blocked by Jason Shackell.
But the main talking point of the opening period was a late tackle by Huckerby on Tierney which could easily have produced a red card and not just a yellow.
Dickson Etuhu was also cautioned but despite the obvious urgency from the home side, Blackpool were still the better team in the opening half.
Even so Etuhu should have headed Norwich into the lead after twenty six minutes but failed to get a proper connection on a Youssef Safri cross.
And the home side were made to pay eight minutes before the break.
Dion Dublin was forced to clear from Parker's dangerous cross and from the resulting corner Jackson headed the ball past David Marshall at the near post.
Parker then had two glorious chances to double the visitors' lead.
But the frontman shot over after racing onto a long ball before the break and was denied by Marshall soon after the restart.
Finally Norwich came to life and Martin almost drew the hosts level seconds after coming on but his shot came back off the post.
Lee Croft's teasing cross was then brilliantly turned over the bar by Barker and Blackpool seemed to be heading through until Huckerby intervened.
Huckerby raced through and curled a superb shot past Evans from 20 yards with 12 minutes remaining.
The home side were now on top and Martin saw a header harshly ruled out for pushing.
And Huckerby looked to have won the game in extra-time when he curled in another sensational right-footed strike past the helpless Rhys Evans.
Blackpool were looking a beaten side but somehow managed to drag themselves level.
Parker had a fine shot tipped over by Marshall but from the corner that followed Barker forced the ball in from close range.
However with penalties looming, Blackpool gifted their hosts the winner.
Hoolahan made a mess of a defensive header and although Chris Brown's initial effort was saved, Martin calmly finished from 12 yards to ensure Norwich will face Chelsea at Stamford Bridge on Saturday.
Norwich City boss Peter Grant:
"They've been terrific over both games and gave us a real scare.
"In the end a couple of bit of quality from Darren Huckerby has been the difference between the two sides.
"I thought Darren was excellent tonight I had a little go at him a few weeks ago for not contributing enough but tonight you saw what he is capable of."
Blackpool manager Simon Grayson:
"We gave a Championship side a really good run for their money.
"It goes without saying that the lads are bitterly disappointed to have lost.
"They put in a fantastic effort and one bit of quality from a really top player was the difference. Huckerby has played at the top level and you can see why."
Norwich: Marshall, Colin (Martin 61), Shackell, Dublin, Drury, Hughes, Safri (Doherty 112), Etuhu, Croft, Brown, Huckerby.
Subs Not Used: Gallacher, McVeigh, Eagle.
Booked: Huckerby, Etuhu, Safri, Marshall.
Goals: Huckerby 78, 95, Martin 112.
Blackpool: Evans, Barker, Jackson, Evatt, Tierney (Gorkss 71), Forbes (Jorgensen 106), Southern, Fox, Hoolahan, Parker, Vernon (Burgess 50).
Subs Not Used: Joseph, Bean.
Booked: Southern, Barker.
Goals: Jackson 37, Barker 108.
Ref: A Marriner (W Midlands).