Spurs only had one shot on target in the opening 45 minutes but it was all they needed to take an early lead through Son Heung-Min, who is now the Premier League's top scorer, before Giovani Lo Celso added their second on 65 minutes.
Poor defending from Pep Guardiola's side on five minutes saw Son left in too much space after a perfectly weighted pass from Tanguy Ndombele. Ederson came out of his goal but Son easily slid the ball under the goalkeeper and into the net.
These early shocks kicked City into gear and they started to put pressure on the Spurs goal.
It seemed like they had got their equaliser on 27 minutes when Gabriel Jesus chested the ball down and took a shot which was deflected into the path of Aymeric Laporte who brilliantly struck the ball into the bottom left corner of the goal.
However, appeals from the Spurs players led referee Mike Dean to check the pitch side monitor for a handball against Jesus. Replays showed the ball had bounced off Jesus' arm and the goal was disallowed.
Lo Celso replaced Ndombele on 65 minutes and scored Spurs' second goal with his first touch of the ball.
Kane ran the ball deep into the City half before laying the ball off to Lo Celso on his left. Once again Ederson was caught rushing out of his goal and, like Son before him, Lo Celso calmly slotted the ball through his legs and into the net for his first Premier League goal.
"It's a season where you've got to do all it takes to win games. It's going to be an up and down year. There's no better feeling when you win. We'll enjoy it, but we know we've got a long way to go," Spurs captain Kane said after the game.
"We're doing well, there's still parts we can improve on. We've got a lot of tough games to go. It's a more open league. Like any season, whoever can put a good spell together will have a good chance of winning."
"It feels good [to be top], but maybe tomorrow we are second again and honestly that would not be a problem for me, I am just happy with the evolution," Mourinho said.
"People cannot expect us to come here and after one season we are fighting for the title. We are not fighting for the title, we are just fighting to win every match. But we are going to lose matches, we are going to draw matches," he added.
Mourinho added Toby Alderweireld, who was substituted off in the 81st minute, had suffered a "bad" muscular injury.
Guardiola's assessment on the match was different this his old rival Mourinho.
"They are top of the league so they are more title contenders than anyone else right now. There are a lot of teams in front of us," Guardiola said.
"I think we are not far, far away [from our best] but we struggle to score goals right now. Ten goals in nine games is not good enough," the Spaniard added.