Their fast start was soon rewarded with the opening goal inside 12 minutes.
Spurs could have levelled nearly instantly but were left disappointed as Dele Alli ended a counter attack with a tame shot at Kasper Schmeichel, something the visitors would be made to pay for before half-time.
The usual suspects were on the scoresheet - for both sides.
With half an hour gone, the Londoners came close again when Christian Eriksen played in Dele Alli, but Schmeichel did well to block.
Leicester were now camped in their own half as Tottenham dominated the ball and territory without testing Schmeichel. "In every position, they have great players", Puel continued.
In an effort to hold onto the point Puel replaced Riyad Mahrez with Ben Chilwell with 20 minutes remaining at the London Stadium, a decision that frustrated the Algeria worldwide. Well it is now despite their second-half efforts and a host of missed chances when they should have actually salvaged this.
Much like the man himself, Claude Puel's start to life at Leicester has been fairly quiet.
With 15 minutes to go, Tottenham and Eriksen wasted a golden opportunity to get themselves back into the game.
And Spurs should have been level when Serge Aurier flashed a cross to the far post, where Llorente somehow managed to divert the ball over the top from six yards out.
It wasn't long before Spurs did then find a way back into the game, courtesy of their talisman, Kane.
He was soon replaced by Erik Lamela, who instantly made his mark by playing in Kane to rifle a right-foot shot past Schmeichel to halve the deficit.
They nearly leveled two minutes later, but Llorente could only fire over from a Serge Aurier cross to waste another guilt-edged chance, although now all the momentum was with the North London side.