England international Kane moved to 26 in the top flight for this season – putting him two ahead of Romelu Lukaku in the Golden Boot standings – while Son took his tally to 21 goals in all competitions in the emphatic victory.
The hammering puts Spurs on 83 points for 2016-2017, three more than Leicester managed when it was crowned champion last season.
Son and Kane combined to put Spurs ahead before the South Korea star made it 2-0 as half-time approached with a well-taken volley.
Ben Chilwell gave Leicester some hope with his first Premier League goal, but a Kane header and a brilliant Son finish ended the Foxes' resistance.
Kane then struck twice in the closing stages to seal the dominant win for Mauricio Pochettino's swashbuckling side.
The defeat, Leicester's 18th of a miserable title defence, saw it miss out on the chance to draw level on points with eighth-place Southampton and did little to enhance manager Craig Shakespeare's chances of holding on to the job for next term.
For Spurs, it was another impressive performance in an excellent campaign that will finish against Hull City on Monday (AEST).