"Tottenham are a great team".
Wilfred Ndidi saw a low strike easily smothered by Hugo Lloris before Leicester captain Wes Morgan, making his 250th appearances for the club, had a header cleared from just in front of the goalline by Danny Rose.
Their fast start was soon rewarded with the opening goal inside 12 minutes.
Both sides will be looking to bounce back from disappointing draws in their last games.
Sissoko was played in by Kane for his opportunity, but could not get the better of Schmeichel and then Vicente Iborra on the line, while Alli's attempt on the break also lacked conviction.
Leicester were now camped in their own half as Tottenham dominated the ball and territory without testing Schmeichel.
Tottenham Hotspur’s Belgian defender Jan Vertonghen and Tottenham Hotspur’s Argentinian midfielder Erik Lamela
"I think he was a little frustrated in the second half without the possibility to touch more balls and to play", said the Frenchman.
The Algerian worldwide cut in from the right before curling the ball out of Lloris's reach from 20 yards out. Well it is now despite their second-half efforts and a host of missed chances when they should have actually salvaged this.
"I don't know when they can come back into the team", he added.
All that changed with 11 minutes to go as Erik Lamela played in Kane with a wonderful pass and the striker blasted high past Schmeichel.
Fellow substitute Fernando Llorente should have equalised three minutes later but somehow poked Serge Aurier's driven cross over the crossbar from inside the six-yard box.
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.