Son Heung-min and Dele Alli were also among the goals for Mauricio Pochettino's side while Mohamed Salah scored for the Reds.
Kane opened the scoring in the fourth minute by slotting into an empty net after beating two defenders and goalkeeper Simon Mignolet in the process.
Son Heung-min doubled the lead for Pochettino's charges in the 12th minute by turning home Kane's cross with a first-time finish that found the bottom corner.
Jurgen Klopp's troops pulled a goal back in the 24th minute through Salah's low finish following a through ball from Jordan Henderson.
Alli restored Spurs' two-goal cushion on the stroke of halftime, pouncing on a poor clearance by Joel Matip with a wonderful volley that found the bottom corner, 3-1.
Kane scored his second goal of the match four minutes before the hour following a goalkeeping howler from goalkeeper Mignolet, 4-1.
Philippe Coutinho produced a great save out of Spurs goalkeeper Hugo Lloris with a thunderous strike from 20-yards out in the 70th minute.
Lloris denied Salah eight minutes later from close range as the Reds were applying the pressure despite trailing by three goals.
Spurs absorbed the pressure in the last 10 minutes to see off Liverpool and move level on points with second place Manchester United.