In front of a Premier League record crowd of 80,827, Spurs stormed into a two-goal lead after just 12 minutes thanks to Kane and Son Heung-min and although Mohamed Salah halved the deficit, a volley from Dele Alli and a second from Kane secured a dominant win for Mauricio Pochettino's side.
The North London outfit now sit on 20 points alongside second-place Manchester United, but Liverpool - who conceded their 1,000th goal in the Premier League - are down in ninth after a crushing defeat.
Kane went into the match having failed to score in four league outings at Wembley, but the in-form striker needed less than four minutes to end that streak after latching onto a pass from Kieran Tripper before rounding Simon Mignolet and bundling the ball into the net.
Liverpool were at sixes and sevens at the back and Spurs soon added a second goal through Son, who volleyed home at the back post from 12 yards out after Kane's pass across the penalty area.
In the 17th minute, the South Korean came agonisingly close to netting a third for his team after running onto a long ball from Christian Eriksen but the attacker's volley cannoned off the underside of the crossbar before bouncing clear.
However, against the run of play, Liverpool halved the deficit through Salah, who ran onto a stunning through-ball from Jordan Henderson before scuffing a shot in off the far post.
Just before the half-hour mark, Son wasted another opportunity with his poked effort going too close to Mignolet and Spurs could have been made to pay with Liverpool dominating the closing stages of the opening period.
Two minutes of added-on time were indicated by the fourth official and with the final action of the half, Spurs scored a third when Alli volleyed into the bottom corner after Joel Matip's clearance went straight to the midfielder, who was waiting 14 yards from goal.
Liverpool needed to get onto the front foot after the restart but it was Spurs who looked more likely to add another and after Kane had glanced a header wide of the far post, the league's top goalscorer had his second of the match.
Spurs were in total control but to Liverpool's credit, they continued to engineer openings at the other end, with Hugo Lloris pulling off a stunning save to prevent Philippe Coutinho's 20-yard attempt finding the top corner.
The Brazilian was denied for a second time soon afterwards, before Lloris got a foot in the way to prevent Salah from adding a second from inside the area.
Chances were few and far between during the closing stages, but there was concern for Pochettino after Kane limped off with what appeared to be a hamstring problem.
The severity of the injury remains unclear, but Pochettino will be delighted with the manner of the victory over a direct rival at Wembley, as well as registering a result which has ended talk of their struggles at Wembley.