Tottenham had failed to score in three of their last six away fixtures but there were no such concerns here as Kane opened his account on 23 minutes when he converted a cut-back from Son, who had sprung the Leicester offside trap.
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.
"You can see with the smile on his face there, he's two ahead now and Lukaku won't be able to sleep tonight". He is great and one of the best strikers in the world.
"I was looking to score a couple of goals, I was looking to take it into the last game, but now I'm in the driving seat", he said.
King remains one of the most popular figures at Spurs even after he was forced to prematurely retire at the age of 31 in 2012 due to ongoing knee problems.
Kane, who is Tottenham's leading scorer this season with 22 goals, scored the last goal at White Hart Lane on Sunday as Tottenham secured second position with a 2-1 win over sixth-placed Manchester United.
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It was his third league hat trick of the season, matching Napoli's Dries Mertens and Bayern's Robert Lewandowski for the most among Europe's top 5 leagues this season. He's the first Tottenham player to accomplish the feat and also the third-youngest after Michael Owen and Fowler.
Son twice had a half-chance on the edge of the Leicester area but it was Jamie Vardy who missed the first good opportunity, striking straight at Hugo Lloris after Riyad Mahrez played him through on goal.
Tottenham boss Mauricio Pochettino: "To be fair when he was injured, other players scored goals, like Son, or (Dele) Alli or (Christian) Eriksen".
"We will keep the players that we want to keep", he said. "Maybe we will sell the players that we want to sell".
"I think the pressure was down, we enjoyed the night".
"We can beat them if we're at our best so Thursday will be an entertaining game".
Despite the fact that the "foxes" spent most of the season as an English champion at the bottom of the standings, risking being in the relegation zone, the results of the spring part made it possible to get out of the situation.
And Leicester manager Craig Shakespeare admitted there was little to take from defeat after the Foxes suffered their heaviest home league loss since 2004.