It is only the third game Spurs have lost in the league all season, and the second at home. Leicester are now joint top of the table after Arsenal drew with Liverpool.
Ex-Chelsea and Stoke City centre back Robert Huth finally broke the stalemate with a well placed header on 83 minutes.
Former Leicester and Tottenham striker Gary Lineker described the goal as 'unbelievable'.
Unbelievable header by Huth and Leicester are winning. Bloody hell I might need to purchase some new pants!— Gary Lineker (@GaryLineker) January 13, 2016
Both sides had made changes after the 1-1 draw at White Hart Lane days earlier in the FA Cup, but the story of frustration was the same for Tottenham.
Harry Kane came close to scoring, wasting a good opportunity in the second half with the game goalless.
Jamie Vardy had returned to the Leicester City side after a short spell out injured, but was withdrawn midway through the second half, without making a major impact.
Tottenham came into the game four points behind Leicester, a gap which has now been extended to seven.