Gareth Bale, who had torn Norwich apart here last season, seemed to have put Spurs on course for victory when he drove home a 20-yard shot in the second-half, but two goals in the last six minutes gave the Canaries an unlikely victory.
First substitute Alex Tettey's shot flew in off the out-stretched leg of Jan Vertonghen and then Simeon Jackson pounced on an error by Hugo Lloris to make it 2-1 with three minutes left. The drama did not end there, however, as Kyle Walker was upended in the Norwich box by Marc Tierney a minute later, but Bunn saved Clint Dempsey's spot-kick.
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. Meanwhile, Bale was a constant threat in an otherwise pretty dull opening 45 minutes.
The second period started with much more purpose, with Spurs looking more dangerous thanks to the introduction of Tom Huddlestone. But Norwich also looked more potent, however, and only a crucial block from Caulker denied Jacob Butterfield his first goal for the Canaries.
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. In response, the home side 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, albeit with a huge slice of luck. Robert Snodgrass' corner fell in to the path of Tettey, whose shot was going wide until Vertonghen inexplicably stuck a leg out to divert the ball 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 lashed past the Frenchman from close range.
There was still time for one last twist, however. Tierney clumsily felled Walker one minute later and 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.
Source: PA
Source: PA