The in-form striker steered the ball low into the corner after Christian Eriksen kept it in play close to the byline on the left to cancel out Philippe Coutinho's opener for the Reds in a lively affair at Anfield.
Kane has now scored 22 league goals for us so far in 2015-16 - more than any other Spurs player in one single season in the history of the Premier League.
Goalkeeper Hugo Lloris had earlier produced a string of fine saves, notably denying Daniel Sturridge and Adam Lallana, twice, in the first half as we produced a determined and gutsy performance.
As far as the team news went, Erik Lamela returned from international duty with a calf problem meaning Heung-Min Son was restored to the starting line-up in the only change from the emphatic win against Bournemouth a fortnight ago.
It was a fairly gentle start from both sides but we soon forced the first opening in ninth minute. A move of quality saw Danny Rose switch the play to Kyle Walker, who pulled it back to Eriksen on the edge of the box and the Dane saw his snapshot well saved by Simon Mignolet.
The home side responded well with Coutinho testing Lloris two minutes later after we surrendered possession in a dangerous position.
Both teams are renowned for their high-intensity pressing style and it meant space and time were at a premium across the middle of the field in a series of frantic exchanges.
Kane came close to what would have been a bizarre goal when he charged down a Mignolet clearance, with the ball ballooning up and behind for a goal kick.
Son almost netted at the wrong end when he slid in to block a cut-back and almost found the bottom corner, but for a fine save from Lloris.
The best opening of the half came in the 26th minute when Mamadou Sakho gave the ball away allowing us to break, Kane led the charge and created an opening for himself but dragged his effort narrowly wide.
With eight minutes of the first half remaining the Reds should have taken the lead when Coutinho slipped in Sturridge but Lloris produced a brilliant save with his legs to deny the England striker one-on-one.
A minute later Lloris was at his best again to parry away an Adam Lallana shot before Kane broke at the other end and looked certain to score until Dejan Lovren produced a fantastic last-ditch block as he pulled the trigger.
It was end-to-end stuff with Lloris then pulling off a wonder save again from Lallana as he leapt at full stretch to claw the midfielder's mis-hit effort away as it looped towards the far corner.
We hadn’t been at our best in the first half but there was a sense that if we could find an extra gear there would be goals for us, particularly with the Liverpool back four making a series of errors.
We had looked in control of the opening exchanges in the second period but, just six minutes in, the home side grabbed the lead. Coutinho rolled in off of the left flank and was found perfectly by Sturridge before the Brazilian slotted past Lloris to open the scoring.
The goal gave the home side a lift and, shortly afterwards, Sturridge might have doubled their lead but he headed over from six yards.
We responded well, though, and almost levelled with what would have been a stunner. Dier spotted the run of Son and clipped a glorious pass into his path, the South Korean international volleyed towards goal first-time and made excellent contact but the ball whistled narrowly past the far upright.
Eriksen then played a key role in our equaliser in the 63rd minute. He refused to give up on a long ball that seemed destined to be heading out for a goal kick and cleverly flicked it back for Kane, who rolled his man and fired across Mignolet and into the bottom corner from the left angle.
Eriksen then brought the best out of Mignolet with a fierce drive from distance that the goalkeeper did well to save.
We suddenly had the wind in our sails and pushed the home side back towards their own goal.
It was still finely poised, though, and Liverpool showed they weren’t done yet as Coutinho fired a wicked shot across the face with 20 minutes to go to swing the momentum back in his side's favour.
Eriksen almost set Alli free at the other end on 78 minutes but the ball ran beyond him after he chested it down on the move and Mignolet was able to gather.
We had a scare on 84 minutes when Reds substitute Divock Origi picked out Coutinho in the box but he hammered wide of the near post from 12 yards out.
Eriksen was then off target with a long-range free-kick after Kane was fouled before Dembele's low drive through a crowded area was tipped wide by Mignolet scrambling down to his left as we entered stoppage time.
We continued to push forward looking for a last-gasp winner with Toby Alderweireld heading wide from Eriksen's corner before Rose wriggled free in the box on the left-hand side and played the ball dangerously across goal but Liverpool were able to clear and we were forced to settle for a point.
Liverpool (4-2-3-1): Mignolet; Clyne, Lovren, Sakho, Moreno; Can, Henderson (c); Milner (Ibe 90+3), Lallana (Allen 82), Coutinho; Sturridge (Origi 72). Substitutes (not used): Smith, Ward, Toure, Skrtel.
Spurs (4-2-3-1): Lloris (c); Walker, Alderweireld, Wimmer, Rose; Dembele, Dier; Son (Chadli 67), Eriksen, Alli (Mason 87); Kane. Substitutes (not used): Vorm, Davies, Trippier, Carroll, Onomah.
Goals: Liverpool – Coutinho 51. Tottenham – Kane 63.
Yellow cards: Liverpool – Coutinho 25, Can 64.
Referee: Jon Moss.