Son Heung-min cancelled out Stuart Dallas' early opener, but Patrick Bamford fired Leeds back in front before half-time and substitute Rodrigo's emphatic finish sealed a deserved victory.
Marcelo Bielsa's side were off colour in last week's defeat at Brighton, but bounced back to turn in another scintillating display against one of the Premier League's 'big six'.
They climbed back into the top half of the table, while Tottenham now face a fight to qualify for even a Europa League place after their first league defeat under interim boss Ryan Mason.
It was soon evident Leeds' energy levels, dimmed at Brighton, had been restored and they created two clear early openings.
Bamford's low shot was turned away by Tottenham goalkeeper Hugo Lloris and Pascal Struijk hooked over the crossbar following a corner soon after.
Leeds were rewarded for taking the game to their opponents in the 13th minute. Lloris saved brilliantly after Jack Harrison's low cross had deflected off Sergio Reguilon and Dallas lashed the rebound into the roof of the net.
Tottenham hit back to equalise with their first shot on target on the counter-attack in the 25th minute. Dele Alli's clever through-ball carved Leeds open and Son raced clear to side-foot home.
Harrison's drive forced Lloris into another save before Harry Kane thought he had given the visitors the lead.
The England striker combined brilliantly with Alli and Son, but his cool, dinked finish was ruled out after the video assistant referee confirmed he had been marginally offside.
It was gripping, end-to-end stuff. Robin Koch's header was deflected wide and then Leeds regained the lead just before half-time through Bamford's 15th Premier League goal of the season.
Ezgjan Alioski charged into the box on the overlap and his inch-perfect cut-back was steered home by the Leeds striker from close range.
Leeds resumed on the front foot at the start of the second half, but Tottenham continued to threaten on the counter.
Kane had another effort ruled out - this time he was clearly offside - and then fired off target before Son crashed a shot into the side-netting.
Alioski's excellent run and cross just evaded Bamford and Mateusz Klich was denied by Lloris, while Illan Meslier produced a superb save to keep out Serge Aurier's near-post drive.
Kane's free-kick then clipped the top of the crossbar, but back stormed Leeds as Toby Alderweireld's brilliant last-ditch block thwarted Klich.
Bamford and Klich then combined well to force another opening, but Harrison fluffed his chance and Klich curled a fine shot just over.
Leeds then made sure of all three points with six minutes remaining when Raphinha's cross was met by a thumping finish from fellow substitute Rodrigo.
It was nothing more than Leeds deserved and they are the first side to remain unbeaten at home in a Premier League season against Arsenal, Chelsea, Liverpool, Manchester City, Manchester United and Spurs since West Ham in 2015-16.