The England striker opened the scoring at the King Power Stadium before providing an assist for Son Heuing-min as Tottenham led 2-0 at the interval.
Leicester halved the deficit midway through the second-half but Kane then scored three goals in the space of 30 minutes to seal a crushing victory for the visitors.
Kane’s performance means he now leads the Golden Boot race by two goals going into the final day of the Premier League season.
As well as leading the race to end the campaign as the top goalscorer, Kane became only the fifth player in Premier League history to score over 25 goals in successive seasons.
Kane, 23, also became only the fifth player to score three or more hat-tricks in a single season in the top-flight.
Second-placed Tottenham travel to the KC Stadium on Sunday to take on relegated Hull City.