Kane struck early in each half, book-ending goals from Son Heung-Min and Dele Alli, with Mohamed Salah netting in reply in front of a record Premier League crowd of 80,827 at Wembley that included the great Diego Maradona.
Spurs move level on points with second-place Manchester United, five points below leaders Manchester City, while Liverpool's sorry defensive display left them a yawning 12 points off the pace in ninth place.
It was a second galling defeat against a supposed title rival for Liverpool, following their 5-0 capitulation at City in early September, and they have now won just one of their last six league games.
They were unrecognisable from the team that had crushed Maribor 7-0 in the Champions League on Tuesday, their travails summed up by a catastrophic defensive display from Dejan Lovren, who was taken off in the 31st minute.
Liverpool's defeat -- their first in 10 league games against Spurs -- also saw them become only the sixth team to have conceded over 1,000 goals since the Premier League was launched in 1992.
With Liverpool out of the League Cup and their hopes of reaching the Champions League last 16 in the balance, it leaves manager Jurgen Klopp facing some uncomfortable questions two years into his Anfield tenure.
His opposite number, Mauricio Pochettino, redeployed the 3-5-2 system he had used in the 1-1 draw at Real Madrid in mid-week, but with illness restricting Eric Dier and Ben Davies to the bench, Serge Aurier started at left wing-back.
Kieran Trippier came into the team on the other flank and within four minutes he had an assist to his name.
The former Burnley man's lofted pass was misjudged by Lovren and with Joel Matip slow to react, Kane stole in, hooked the ball inside the advancing Simon Mignolet and rolled it into the net.
Lovren's nightmare continued eight minutes later as he woefully mistimed an attempt to head away a long throw from Spurs goalkeeper Hugo Lloris, allowing Kane to canter into the space behind him.
- Alli volley -
The England striker found Son with a brilliant cross from the right and the Spurs number seven used the inside of his left foot to plant a first-time shot past the exposed Mignolet.
It was almost 3-0 moments later as Son chested down Christian Eriksen's through ball and slammed a shot against the Liverpool bar.
Liverpool reduced the arrears against the run of play in the 24th minute when Jordan Henderson's pass from deep released Salah to trundle a right-foot shot past Lloris and in off the left-hand post.
But Spurs continued to find space behind Lovren -- Son's toe-poke blocked by Mignolet after he was cleverly freed by Alli -- and in the 31st minute Klopp brought the Croatian's torment to an end.
Alex Oxlade-Chamberlain came on and the ensuing reshuffle meant Emre Can dropped to right-back, where he was quickly found wanting.
His untidy foul from behind on Alli gave Spurs a free-kick in first-half stoppage time and when Eriksen's delivery was headed away by Matip, Alli thumped a volley into the bottom-left corner.
It was game over 11 minutes into the second period after yet more scenes of calamity in the Liverpool penalty area.
Mignolet flapped at Trippier's free-kick and although Roberto Firmino got back to block Jan Vertonghen's goal-bound shot, Kane reacted swiftly to crash the rebound home.
With eight goals, the 24-year-old is now the outright top scorer in the division.
A second goal eluded Liverpool, Lloris acrobatically tipping a Philippe Coutinho curler onto the post and saving with his feet from both James Milner and Salah.
Kane went off holding the back of his left leg late on, but Pochettino said he was merely "tired".