City, who had not dropped a point in their previous six games, went behind when Aleksandar Kolarov diverted a cross from Danny Rose past his own keeper on nine minutes.
Dele Alli added a second after good work from Son Heung-min and, with City failing to cope with Spurs' pressing and pace, the home side also had an Erik Lamela penalty saved by Claudio Bravo.
No doubt regular spot-kick taker Harry Kane would have done better, but in every other respect Spurs coped well without their striker as South Korea's Son produced another dazzling performance.
By contrast, City struggled without their own missing man, Kevin De Bruyne, who had inspired their scintillating start to the season.
Gardiola was gracious in defeat, admitting Spurs had been the better side.
"We were little late in all aspects. We could not have so many chances, in many aspects they were better than us," he said.
"They are sharper for the second ball, in England you have to control that. Football is 90 minutes, we had a good start but we didn't have the game. We had problems to control the game."
Manchester United also had a frustrating afternoon as Stoke registered their first point at Old Trafford since 1989 when Joe Allen popped up late to slot home the equaliser in a 1-1 draw. His second goal in consecutive games moved the visitors off the bottom of the table above Sunderland and eased some of the pressure on manager Mark Hughes.
Once again Jose Mourinho chose to start Wayne Rooney on the bench, bringing him on in a double substitution with Anthony Martial. Within two minutes United were ahead, although it was the Frenchman, not England's record scorer, who netted.
Despite the result, which left United three points worse off than at the same stage last season under Louis van Gaal, Mourinho said it was United's "best performance of the season".
"It was much better than against Leicester (when United won 4-1 last week). It could have been 3-0 or 4-0 at half time, 6-0 at the end of the game, but the result was 1-1. But that's football."
Leicester City drew 0-0 at home to Southampton, who have now gone six games without conceding a goal. Charlie Austin came closest to scoring, hitting the post with a first-half effort.
(Editing by Pritha Sarkar)
