The giant German defender struck seven minutes from the end of a pulsating game that meant so much to both teams’ hopes of Champions League football.
And it was the visitors who came out on top, having been denied victory by a late Harry Kane penalty in the FA Cup at the same ground on Sunday.
This time there was to be no comeback for Spurs, who are still in the top four but only a point above West Ham after this, their third defeat of the season.
While the lack of goals must be a concern to Mauricio Pochettino, Claudio Ranieri was able to welcome back his talisman and top scorer Jamie Vardy after a speedy comeback from injury.
Both managers made wholesale changes to the sides that had drawn 2-2 here on Sunday, and the most significant return was that of Vardy in the Leicester attack, less than a fortnight after undergoing hernia surgery.
The Leicester forward did not look back to full pace however, and it was his strike partner Shinji Okaxaki who looked more likely to open the scoring for Leicester. The little Japanese forward had a dipping volley tipped away brilliantly by Hugo Lloris in the 25th minute.
But Kasper Schmeichel was just as busy — and brilliant at the opposite end to keep Tottenham at bay. The Leicester keeper’s first great save came in the tenth minute when he tipped a header from Toby Alderweireld over the bar. He then made an even better save, diving full length to push away a fierce drive from Christian Eriksen after the Dane had been set up by Harry Kane.
The game was a fasinating contrast of styles, with Tottenham’s slick passing football up against Leicester’s more direct, counter-attacking style. Both have their merits, both created chances.
Referee Lee Mason showed remarkable lenience to keep his cards in his pocket for so long, especially in the face of some strong tackling from Leicester, with Danny Simpson and Wes Morgan particularly lucky to escape punishment.
But the majority of the game was played in a cup-tie spirit, hardly surprising since both sides were craving victory.
Leicester had a good spell immediately after half-time, winning corner after corner as Tottenham struggled to get the ball out of their half. Vardy had a close-range shot defected over the bar, and was then denied by Lloris saving at his feet, before departing soon afterwards to be replaced by Leonardo Ulloa.
Schmeichel continued to be the busier keeper. Kane was put through and hit a powerful shot that the Dane tipped onto the crossbar after an hour, and then he made an even better save to keep out a piledriver from Dele Alli.
Mauricio Pochettino made changes to try to tease a goal for Tottenham, sending on Mousa Dembele, but out of the blue it was Leicester who scored the all-important goal. After winning a corner on the left in the 83rd minute, Christian Fuchs floated in an outswinging cross towards the far side of the penalty area, where Huth, unmarked, steered a powerful header back into the opposite corner of goal.
Leicester’s players celebrated wildly with their supporters tucked into a corner of White Hart Lane, and they responded with chants of “We’re going to win the league” and “We’re all going on a European tour”.
Spurs threw everything they had at the visitors in the final minutes, which included four minutes of stoppage time, but they could find no way past Schmeichel and his magnificent defence.
Pochettino has made no secret of his desire for another striker to support Kane, and Tottenham’s hopes of a Champions League spot may well depend on how Daniel Levy performs in this month’s transfer window.
But Ranieri has no such worries, and with the squad and spirit he has at his disposal, can start making serious plans for a European challenge next season.
And if they keep surprising people like this, who would bet against them going all the way?
Lloris 7, Walker 6, Alderweireld 7, Vertonghen 6, Davies 6; Carroll 6, Dier 6; Lamela 7, Eriksen 6, Alli 7; Kane 6 Substitutes: Dembele fro Eriksen 69, Onomah for Dier 89, Son for Carroll 81.
Schmeichel 9, Simpson 6, Morgan 7, Huth 7, Fuchs 6, Mahrez 6, Kanté 7, Drinkwater 7, Albrighton 6, Okazaki 7, Vardy 5 Substitutes: King for Okazaki 76, Ulloa for Vardy 69, Dyer for Mahrez 89.