City, who had won their first 10 matches of the season under new manager Pep Guardiola before drawing 3-3 at Celtic in the Champions League on Wednesday, remain top of the table but could not cope with the intensity, pace and pressing of Spurs, who now sit second, only a point behind.
The home team went ahead in the ninth minute when Aleksandar Kolarov put Danny Rose's long cross into his own net and an unmarked Dele Alli doubled the lead before halftime.
In the second half Claudio Bravo saved Erik Lamela's penalty to prevent an even heavier defeat.
It was an outstanding performance by Mauricio Pochettino's side, who left to a thunderous ovation and must now be convinced they can at least repeat last season's challenge for a first title since 1961.
Although without injured England striker Harry Kane, Spurs had a newly confident Son Heung-min in fine form as leader of the attack after scoring three times in his last two games.
The South Korean international set up the second goal and led the way as City were relentlessly harried and often pressed into mistakes while trying to play out from the back.
Guardiola's hopes of becoming the first manager to win his first seven Premier League matches looked shaky from the start under an early onslaught.
His team contributed to their own downfall, however, when in the ninth minute Kolarov completely misjudged Rose's diagonal cross and found his own net.
Seven minutes before halftime the marking was non-existent as Son, collecting the ball as it bounced off defender Pablo Zabaleta, fed Alli for a composed finish.
Leading scorer Sergio Aguero came closest for City but was twice thwarted in the second half by good saves from Tottenham captain Hugo Lloris.
The damage could have been worse, for in the 65th minute City conceded a penalty when Alli was tripped by Fernandinho, but Claudio Bravo beat away Lamela's penalty.
"They were better than us today and we have to say congratulations to Tottenham," said Guardiola.
(Editing by Pritha Sarkar)
