The visitors, who had won ten of their previous 11 games under the Spaniard, were far from their best and were behind after just nine minutes through an Aleksandar Kolarov own goal.
Dele Alli then finished off a fine team move to double Spurs’ lead with a low shot before half-time.
Tottenham continued to control the game well after the break and could have made it 3-0 when they were awarded a penalty, but Erik Lamela saw his effort saved by City goalkeeper Claudio Bravo.
City, meanwhile, struggled to create clear-cut chances without the injured Kevin De Bruyne and did little to threaten Hugo Lloris in the Spurs net.
The win saw Tottenham move back above Liverpool into second place and close the gap on early pace-setters City to just one point.
It was an enticing clash as the Premier League’s only remaining unbeaten sides went head-to-head in north London, and also saw the top flight’s best defence go up against the most potent attack.
But City, who had scored 18 goals in their opening six games, drew a blank at the Lane while steadfast Spurs took their chances well.
Spurs started well in what was a high-tempo first-half and quickly took the lead thanks to an unfortunate error from City full-back Aleksandar Kolarov, who shanked a clearance from Danny Rose’ dangerous cross into his own net.
The difference between this City and the team who looked unbeatable just a few weeks ago was startling in the opening half. They looked nervy at the back, particularly when faced with the lively Son Heung-min, and just could not cope with Spurs’ intensity.
And it was that high-tempo which led to Spurs’ second as Alli took advantage of sluggish defending to score what eventually proved to be the game-clinching goal.
A flowing Tottenham counter-attack move had appeared to have broken down, but the City defence were then caught out by a clever reverse pass from Son to Alli, who burst through three players to meet the ball and fire hard and low past Bravo.
Tottenham continued to pile on the pressure after the break, with Son and Victor Wanyama both going close to a third goal, before Lamela had his spot kick well saved by Bravo after Alli was clumsily fouled in the box.
City produced their best chance of the game late on as Sergio Aguero, who was kept quiet by the Spurs back-four, was sent free by a Fernandinho pass, but the Argentine’s shot was parried by Hugo Lloris onto the crossbar.