It was a goal to grace any stage and the highlight of what had been a scrappy encounter in tough conditions, a swirling wind and dry playing surface making it difficult to sustain any possession.
Norwich took advantage and were the better team in the first half, rewarded by Wes Hoolahan's 33rd-minute opener.
We responded well in the second half. Lewis Holtby made a promising debut after entering the fray on 71 minutes and Bale finally produced his moment of magic with 10 minutes remaining, running fully 60 yards before planting the ball in the far corner.
It was his fourth goal in our last three appearances at Carrow Road and stretched our run to one defeat in 12 in the Premier League.
Mark Bunn in the Canaries' goal denied us a dramatic late winner by tipping aside Gylfi Sigurdsson's 20-yarder in the final minute.
Andre Villas-Boas made five changes to the team that started at Leeds on Sunday.
Hugo Lloris returned in goal, Michael Dawson was back in central defence and they were joined by Kyle Walker, Mousa Dembele and fit-again Jermain Defoe. Norwich made eight changes after their FA Cup exit against Luton.
The first half was far from a spectacle as the home side made the most of the conditions.
As expected, we were tested aerially and to the most part, coped well with the threat of Grant Holt. Lloris had to be on his guard to deal with a moving ball but there were few clear-cut chances at either end.
Bale headed wide from Walker's corner, Seb Bassong did well to shepherd Clint Dempsey away from a dangerous position and Holt fired high and wide before the first save, Lloris down to his left to turn aside Holt's downward header on the half-hour.
The opener arrived three minutes later. Holt did well to guide a deep cross back to Anthony Pilkington and he drilled across goal where Hoolahan swept home from 12 yards.
Our best chance arrived just before half-time as the ball broke to Aaron Lennon from Michael Turner's challenge, he rolled into Defoe whose snapshot was turned away by Bunn.
There were no substitutions at the interval but a tactical change for the second half as Bale moved centrally alongside Defoe and Dempsey to the left.
That switch enabled us to gain a territorial advantage but chances were still at a premium.
Bunn was equal to Bale's crisp drive on 51 minutes and the teams traded shots wide, Dempsey and Pilkington off target, as we slowly pushed the home side back.
Holtby replaced Dempsey for his debut on 71 minutes and was soon on the ball, knitting passages of play together with Dembele.
And the new arrival who only trained with the team for the first time on Tuesday played his part in Bale's latest masterpiece.
Seemingly going nowhere on the left touchline, Holtby backheeled the ball into the path of Defoe on half-way. Defoe flicked into the path of Bale, who took the ball in his stride, somehow stayed on his feet after Alex Tettey's challenge and then drove forward 50 yards into the box. He then sidestepped Javier Garrido before firing into the far corner.
It was now all Spurs. Defoe flicked Assou-Ekotto's cross just over and with a minute left, Sigurdsson's sweet strike looked destined for the bottom corner before Bunn, at full stretch, tipped it wide.
Norwich City (4-4-2): Bunn: Martin, Bassong, Turner, Garrido; Snodgrass, Johnson, Tettey, Pilkington; Hoolahan (Howson, 80), Holt. Unused subs: Camp, Whittaker, R Bennett, Jackson, Fox, E Bennett.
Spurs (4-4-1-1): Lloris; Walker, Dawson, Vertonghen, Assou-Ekotto; Lennon (Sigurdsson, 87), Dembele, Parker, Bale; Dempsey (Holtby, 71); Defoe. Unused subs: Friedel, Caulker, Gallas,
Yellow cards: Norwich - Garrido, Holt, Snodgrass, Hoolahan. Spurs - Holtby.
Goals: Norwich - Hoolahan (33). Spurs - Bale (79).
Referee: Mr N Swarbrick.