For much of the game, home manager Chris Hughton never looked like beating the club with whom he played for 14 years.
Apart from an early opportunity from Steve Morison, who was denied by a crucial block from Steven Caulker, the Canaries were the second best team for most of the first half.
After a slow opening 10 minutes from both sides Andre Villas-Boas shuffled his pack by swapping Gareth Bale on to the right to give him a run at Marc Tierney.
The Norwich left-back struggled to keep his composure, mis-placing a header that allowed Bale to charge at the Canaries defence but he shot straight at Mark Bunn.
The Welshman got the better of Tierney moments later and found Clint Dempsey, but the American’s clever chip sailed just over Bunn’s goal.
Bale then rippled the Norwich side-netting from a Jake Livermore cross and shot inches wide soon after as the winger threatened to open the home side up.
Jonny Howson flashed a volley two yards wide just before referee Jon Moss brought the dull opening half to a halt.
The second period started with much more purpose, with Spurs looking more threatening thanks to the introduction of Tom Huddlestone.
Norwich also looked more potent, however, and only a crucial block from Caulker denied Jacob Butterfield.
Falque almost caused Morison to put through his own goal thanks to a wicked cross and the Spaniard then played in Bale only to see the winger shoot straight at Bunn.
The stopper had to be at his best to deny Falque’s brilliant curling shot, but Norwich then flew up the other end through Morison, who was denied by some quick thinking from Hugo Lloris.
Norwich were playing with much more confidence, but their hopes of an upset took a hit in the 66th minute when Bale latched on to Tom Carroll’s pass and drove a sweet right-footed drive past the diving Bunn.
Hughton’s team responded well. With Alex Tettey and Simeon Jackson drafted on from the bench, the hosts pushed for an immediate equaliser and they almost got it when Howson’s wicked shot needed an acrobatic save from Lloris.
Norwich piled on the pressure and Hughton took one last throw of the dice when he brought on captain Grant Holt.
The pressure told as the home side equalised as Spurs substitute Jan Vertonghen inexplicably stuck a leg out to divert Tettey’s wayward shot past Lloris.
Tottenham’s heads dropped, but worse was to come.
With three minutes left Lloris spilled Holt’s header straight at the feet of Jackson, who geefully lashed past the Frenchman from close range.
There was still time for one last twist, however.
Tierney clumsily felled Kyle Walker one minute later and referee Moss pointed to the spot.
Dempsey stepped up to take the spot-kick, but Bunn saved well to his left, causing ecstatic scenes among the home support.
NORWICH: Bunn, Whittaker, Turner, Ryan Bennett, Tierney, Snodgrass, Fox (Tettey 68), Butterfield (Jackson 68), Surman (Holt 82), Howson, Morison.
TOTTENHAM: Lloris, Walker (Defoe 90), Dawson, Caulker, Naughton, Sigurdsson, Livermore (Huddlestone 46), Carroll (Vertonghen 79), Falque, Bale, Dempsey.
Ref: Jon Moss (W Yorkshire).