City are on 53 points, seven clear of second-placed Leicester City, who beat Liverpool 3-1 earlier on Saturday, and with a game in hand.
Pep Guardiola’s side have now won 16 straight matches in all competitions and German Gundogan has been central to that record-breaking run of form with 11 goals in his last 12 Premier League outings.
Jose Mourinho’s Spurs went close to opening the scoring through a Harry Kane free kick, a curling effort over the wall, that struck the bar.
Yet City went in front in the 23rd minute with a Rodri penalty after Gundogan was tripped in the box by Pierre-Emile Hojbjerg.
From then on there was only one team going to win the encounter as City turned on their dominant passing game and Spurs had little in response.
Gundogan made it 2-0 five minutes after the interval, beating Hugo Lloris at the near post after good work from Raheem Sterling.
Then the former Borussia Dortmund midfielder, revelling in a more advanced midfield role, completed the win when he latched on to a superb long ball forward from goalkeeper Ederson, before putting Spurs defender Davinson Sanchez on the floor with some clever footwork and slotting home.
Spurs are in eighth place, four points adrift of the fourth Champions League spot.