Wes Hoolahan had given the out-of-form Canaries a half-time lead, but Bale rescued a disappointing Spurs display with his 80th-minute individual effort.
The result leaves the visitors one point clear of Everton in fourth, while Norwich remain 14th in the Premier League table.
Below, Sports Mole analyses whether the result was reflective of the action in East Anglia.
On target: 4
On target: 7
Was the result fair?
Probably not. Spurs were second best in every department, apart from left wing that is. Norwich will feel very hard done by considering their first-half efforts but then again, a goal of Bale's quality does not deserve to be in a losing cause.
A very good team display, especially bearing in mind their recent form, which has seen them winless in six top-flight matches. Their midfield worked incredibly hard and their constant pressuring on the ball prevented Spurs from playing their normal passing game. Anthony Pilkington and Robert Snodgrass were threatening presences down the flanks and often got in behind the visiting full-backs.
As poorly as they will have played this season. Shaky in defence, particularly in the wide areas, Benoit Assou-Ekotto was regularly caught out of position and his sloppiness resulted in the Norwich opener. There was no intent to their passing in midfield and Aaron Lennon and Jermain Defoe both had off-days in the final third. Andre Villas-Boas will be thankful that Bale is as good as he is.
Sports Mole's man of the match
Gareth Bale: And he is very good. Norwich were excellent collectively, but there was no standout performer and Bale's individual brilliance single-handedly earned Spurs a point.
Villas Boas's hesitation in making changes. Spurs were awful for 75 minutes and yet it took that long for the Portuguese to turn to his substitutes' bench. When he did, debutante Lewis Holtby and Gylfi Sigurdsson had an impact and the latter would have snatched a winner had it not been for a Mark Bunn wondersave.
Neil Swarbrick had a good game, correctly turning down two Norwich penalty appeals and only going to his pocket when necessary.
Norwich: An away trip to Queens Park Rangers, where a win would ease their increasing worries of being dragged into a relegation battle.
Spurs: West Bromwich Albion at the Hawthorns on Sunday. But before that, maybe some transfer-deadline-day drama?