The Blues looked well on their way to all three points at Stamford Bridge after goals from Kalidou Koulibaly and Reece James came either side of an equaliser from Spurs midfielder Pierre-Emile Hojbjerg.
But Kane popped up deep in injury-time and grabbed an equaliser for his side as his flicked header was diverted into the net by England team-mate Reece James.
The result meant Antonio Conte’s side built on their opening day win against Southampton and earned a draw at a ground where they have found points hard to come by during the Premier League era.
“I think it was a really important game for us to show where we are as a team,” the England captain told Sky Sports.
“It’s a marathon this season, not a sprint, and we have a long way to go with the World Cup in-between.
“But I think it was important after losing five or six times to them in the cup and Premier League.
“Away at Stamford Bridge hasn’t been our best place over the years, so to come away with a point at the end is a good feeling.”
Kane reflected on his point-saving moment as he claimed a draw right in front of the travelling Spurs support and praised his team-mates for a ‘fighting’ performance.
“A really tough game playing against a really good side,” explained the striker.
“Like I said before, we knew it was going to be a tough battle.
“First-half, we weren’t good enough with or without the ball, but second-half, I thought we pressed well, we got the goal, disappointed to concede the second, but we carried on fighting.
“Thankfully, we got one at the end there.
“I kinda flicked it and I couldn’t really see where the ball went, I just saw the net rustling right in front of our fans.
“I had that chance earlier in the second-half, it was nice to see that one go in.”