Blackpool kicked off attacking the River End goal, urged on by a vociferous band of travelling fans.
Huckerby was booked after seven minutes for a foul on Paul Tierney and Chris Brown fouled the same player a minute later, but escaped a booking.
Dickson Etuhu did get booked for his challenge on Keigan Parker after 17 minutes.
Brown then got a touch to Adam Drury's driven pass but the ball went wide. His next shot was blocked as the visitors defended in numbers.
Blackpool went ahead in the 37th minute when an in-swinging left-wing corner from Fox was headed in at the near post by skipper Michael Jackson.
It might have been worse for the home side because Parker's shot was only inches away from the angle of post and bar, before David Marshall saved Keith Southern's long-range effort.
In the opening exchanges of the second half Jason Shackell's header was cleared for a corner.
Marshall did well to hold Parker's shot at the second attempt. Parker was then booked for dissent following his foul on Dion Dublin.
The Tangerines were then put under heavy pressure and Southern was booked for a foul on Safri.
The Canaries drew level when Huckerby cut in from the left wing and unleashed a fierce right-foot drive that flew into the top left-hand corner of Rhys Evans' goal from 20 yards.
Norwich looked to have won the game in the 87th minute when Martin headed Safri's free-kick into the net, but referee Andre Mariner ruled it out.
As the game went into stoppage time Evans saved Andrew Hughes' shot taking the match into extra-time.
Norwich kicked off for the first period, attacking the Barclay End goal and it was no surprise when Huckerby repeated the shot that had brought City level, in the 95th minute, this time from 16 yards.
Norwich regained the lead for the final time when Martin steered a right-foot shot inside Evans' left-hand post from 12 yards after Ian Evatt had blocked Brown's shot.