Kane's header deep into stoppage time seconds after the hosts had levelled through Riyad Mahrez's penalty inflicted City's first league defeat in 16 video games.
Liverpool can now close to inside 3 points of the leaders need to they win their sport in hand at home to Leeds on Wednesday.
The comparison in form among the sides could not were starker as Tottenham had lost their previous 3 league games.
But Antonio Conte prevented losing 4 at the bounce for the primary time in his managerial profession way to a dogged protective show enlightened by means of flashes of brilliance with the aid of Kane and Son Heung-min at the smash.
Had Kane had his way remaining summer time, he would have been lining up in blue as opposed to Tottenham white.
He was City's top target to replace membership file goalscorer Sergio Aguero, however it was Kane's playmaking capability that stuck the attention in the first half of.
Conte claimed Tottenham were weakened in the January switch window in his modern-day withering take on the capacity of his squad to Italian media this week.
Both of Spurs' January signings Rodrigo Bentancur and Dejan Kulusevski started out and it turned into the Swede who gave the visitors a dream start.
Kane's sumptuous through ball broke City's offside lure and Son unselfishly squared for Kulusevski to slot into an unguarded internet after simply 4 minutes.