Wes Hoolahan had given the Canaries a deserved first-half lead as Tottenham failed to make an impact on the opening period. An improved second-half effort salvaged dignity, however, as a stunning individual strike from the Welshman pulled Spurs back onto level terms.
Sebastian Bassong returned from a calf injury to start for the hosts against a side he previously made 72 appearances for, but loanee Harry Kane was ineligible to start against his parent club.
Meanwhile, Andre Villas-Boas was able to name new signing Lewis Holtby on the bench, with Jermain Defoe making the starting lineup despite worries about a pelvic injury.
A quiet opening period saw neither side make a distinctive mark on proceedings, with the first notable moment coming in the 20th minute when Grant Holt fired a shot way over the bar.
Holt was involved again just three minutes later when the home side cried out vociferously for a penalty, but the referee was unwilling to entertain the appeals.
The home side had shaded the opening half hour and came close on 29 minutes when Hugo Lloris was forced to tip a header wide of the Tottenham goal.
Norwich was rewarded for its efforts just three minutes later when Hoolahan slotted home his second goal of the season after Anthony Pilkington had received the ball from a Robert Snodgrass cross and squared to Hoolahan in the area.
The home side then almost doubled the lead as Bassong charged through the middle to latch on to a low cross from Snodgrass but was denied by a block from Benoit Assou-Ekotto.
Spurs soon enjoyed their own period of attacking dominance and almost grabbed a quick equalizer as Defoe robbed Bassong of the ball at the other end and advanced on goal, only to have his shot stopped by a terrific save from Mark Bunn.
Norwich held onto their lead until the break and began the second half a similarly positive manner.
However, Tottenham was looking a much sharper side after the break and eventually the club's pressure paid off.
Just as Spurs looked like they were running out of options, Bale – who scored two against Norwich last season – made a fantastic run into the box and smashed a left-footed shot straight into the top corner.
Spurs looked the more likely side to snatch a late winner and substitute Gylfi Sigurdsson almost grabbed it with a shot from distance, but Bunn produced another fantastic save and the affair finished all square.
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