In front of 80,827 fans, the biggest ever Premier League attendance, Kane took his league tally to eight for the season with the first and fourth goals in a clinical Spurs display.
Son Heung-min and Dele Alli were also on target for the impressive hosts, who led 3-1 at the break after a breathless first half, while Mohamed Salah’s reply had briefly given Juergen Klopp’s Liverpool side hope.
Tottenham’s fourth consecutive victory, and first in the Premier League against Liverpool for five years, put them level on 20 points with second-placed Manchester United and five behind rampant leaders Manchester City.
Liverpool dropped to ninth on 13 points and have conceded 16 goals — their highest total after nine games since 1964.
“The whole game the whole result was all our fault — Tottenham were good, they needed to be good, but we made it much too easy for them,” said Klopp, who reacted by hauling off hapless defender Dejan Lovren after 31 minutes.
Both sides were buoyed by superb midweek results in the Champions League with Mauricio Pochettino’s Tottenham team fresh from a 1-1 draw away to European champions Real Madrid and Liverpool having scored seven goals at Maribor.
It was the home side who began in razor-sharp fashion in front of watching Argentina great Diego Maradona though, albeit aided by a porous Liverpool rearguard.
In the fourth minute, Spurs defender Kieran Trippier played Kane into acres of space and the England striker cleverly dinked the ball around goalkeeper Simon Mignolet with his right foot before guiding a shot home with his left.
Tottenham were two goals up inside 12 minutes, this time Lovren inexplicably failed to cut out Spurs keeper Hugo Lloris’s long throw to allow Kane to advance and calmly square for Son to stroke the ball home left-footed.
Liverpool’s defence parted again to allow Son in on goal soon afterwards but his fierce effort struck the crossbar.
Tottenham’s defence dozed off in the 24th minute, enabling Salah to get between them and latch on to Jordan Henderson’s pass. With Lloris slow to narrow the angle, the Egyptian scuffed his shot in off the post.
The visitors then began to enjoy the lion’s share of possession but their defence continued to creak and Lovren was replaced by Alex Oxlade-Chamberlain.
It made little difference though as Spurs took advantage of more woeful defending in first-half stoppage time.
Christian Eriksen floated in a free kick which Joel Matip could only head tamely straight to Alli who volleyed past Mignolet from inside the area.
In the 56th minute, Mignolet flapped at Trippier’s inswinging free kick, Jan Vertonghen’s shot was cleared off the line by Roberto Firmino but it fell to the lurking Kane who steadied himself before drilling into the corner.
There was no way back for Liverpool, although Lloris did have to pull off an incredible one-handed save to push Philippe Coutinho’s powerful effort against the bar and later blocked a Salah shot with his legs.