Foreshadowing their imminent goal spree, Tottenham started with a swagger and almost took the lead when Kane's pass picked out Son, only for Chilwell to deny him with a last-ditch block.
Son then made it 4-1 with a superb finish in the 71st minute before Kane completed his hat-trick with a powerful drive from the edge of the area in the 88th minute.
"We had been talking about (the season not being over) during the weekend".
The goal, Son's 20th of the season, marked the first time three Tottenham players had passed that mark in a season with Alli on 21 and Kane now netting 32.
It is incredible to think that Alli was playing League One football with the Buckinghamshire outfit just two years ago, and his rise within the game has been quite a seismic one.
Harry Kane admitted the Premier League Golden Boot was on his mind as he hit four goals in Tottenham's thumping 6-1 win at Leicester.
The England worldwide netted four times in Thursday's 6-1 rout to take his tally for the season to 26 and move two clear of Romelu Lukaku in the goalscoring charts.
The English striker is the highest goalscorer in the English Premier League this season with 26 strikes.
Harry Kane and Son Heung-Min accounted for all of Tottenham's goals on Thursday night.
Kane has now scored 32 in all competitions and 26 in the league. "Every player really enjoyed the game", said Son. "Maybe we will sell the players that we want to sell".
"I felt good, Leicester made it tough for us, they put the pressure on to get the goal back, but to get that third goal was vital and the game opened up". "We are building a very exciting project".
"I am in the driving seat", said Kane of the Golden Boot standings.
"They are an excellent side, I knew that before the game, but obviously we were totally second best".
Shakespeare also challenged his players to make amends by ending the season with victory over Bournemouth, which would allow them to finish in the top half of the table.
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