Wes Hoolahan's 32nd-minute goal gave the Canaries a deserved lead, but Spurs winger Bale equalised after 80 minutes with a scintillating run from his own half which he finished off with a shot into the bottom corner.
Substitute Gylfi Sigurdsson was denied by Mark Bunn after 89 minutes as Tottenham finished the stronger but had to settle for a point.
Norwich were much improved following the humiliating 1-0 FA Cup fourth-round loss to Luton, but were left to rue a missed opportunity after dominating the opening 45 minutes.
Chris Hughton will hope additions up front - with Sporting Kansas City's Kei Kamara joining, paperwork permitting - can end their streak of two points from 21 in the Premier League at QPR on Saturday.
Spurs, too, are looking for a cutting edge in the final 24 hours of the transfer window and Bale's intervention, his 12th goal of the season, proved invaluable once more.
Norwich started with purpose and energy in contrasting fashion to last Saturday's lacklustre display against Luton, which was not surprising given manager Hughton made nine changes, reverting to his first-choice XI.
The Canaries were boosted by the return of Sebastien Bassong against his former club, with the muscular defender opposed by Jermain Defoe as one of five changes to the Spurs side which lost at Leeds on Sunday. New signing Lewis Holtby was among the substitutes.
Tom Huddlestone was not alongside him, adding to speculation the midfielder could leave before the close of the transfer window.
Defoe blocked Bunn's clearance with his back in the opening skirmishes, provoking a collective gasp from home supporters, but it was the Canaries who looked more enterprising.
Robert Snodgrass was proving a useful source of supply down the right, while Bassong and Michael Turner kept Spurs quiet at the other end.
Grant Holt blasted well over from outside area before tumbling between Jan Vertonghen and Benoit Assou-Ekotto only for referee Neil Swarbrick to ignore appeals for a penalty which appeared to be made more in hope than expectation.
Holt had another header scrambled clear by Hugo Lloris after Michael Dawson failed to deal with a bobbling ball in the area following a Snodgrass cross.
It was a Snodgrass cross which led to the opener after he was freed by Russell Martin down the right. The ball was too high for Holt at the far post, but he flicked it to Anthony Pilkington, who was composed enough to play it centrally to Hoolahan to slot in between a ramshackle Spurs defence and a floundering Lloris.
A Javier Garrido foul on Bale earned a yellow card, but the resulting free-kick sparked a Norwich counter-attack led by a rampaging Bassong.
Snodgrass found the overlapping Martin, whose cross towards Bassong was blocked by Mousa Dembele.
Bassong was indebted to his goalkeeper soon afterwards.
Defoe nipped in front of the defender, played a one-two with Aaron Lennon and then shot, with Bunn saving smartly.
Norwich showed further intent on the resumption and Martin's dangerous cross narrowly evaded Hoolahan in the box.
That belatedly sparked Spurs into life, but the Canaries defence repelled the visitors.
A well-timed Turner tackle dispossessed Defoe and Bale shot low for Bunn to save soon afterwards.
Defoe and Pilkington exchanged shots before a Snodgrass foul on Assou-Ekotto earned Spurs a free-kick in a promising position and the Scot a yellow card for dissent.
Turner cut out Walker's set-piece and a Dembele cross before the ineffective Clint Dempsey was replaced and Holtby came on for his debut.
The Germany international neatly linked up play before he was booked for dissent after Bunn had clawed a Lennon cross out of the air with Bale lurking.
Bale needed no assistance for the equaliser. He picked the ball up inside his own half and raced by Alex Tettey and into the area, cutting onto his left foot to shoot by Garrido and Turner and beat Bunn.
Tottenham pressed on in search of a winner in the final 10 minutes.
Bunn saved a swerving effort from Sigurdsson, on for Dempsey, which deflected off Bassong and used his feet to deny Bale from the resulting corner as the match ended level.