The 22-year-old came off the bench on Sunday to score a last-gasp penalty and earn Spurs a 2-2 draw and an FA Cup third-round replay at Leicester next week.
With Kane one of a number of players rested by Mauricio Pochettino, Tottenham looked to be heading out after goals from Marcin Wasilewski and Shinji Okazaki had cancelled out Christian Eriksen’s opener.
But Kane was called upon with a little over 20 minutes remaining and slammed home an 89th-minute penalty after Nathan Dyer was adjudged to have handled in the box.
Pochettino played down reports the England striker had emerged as a target for Real Madrid last week and Kane himself insists his future lies in north London.
“Yes, definitely,” he replied when asked if Tottenham was where he wanted to spend his long-term future.
“There are always going to be rumours flying around but I’m happy here.
“The club is in a good shape, we have a great future and I’m raring to go so we will see what happens.
“We have got a lot of young players raring to go who are getting better and better with each game and that is all we have got to do.
“Keep working hard on the training field, we are getting better and more experienced the more we play and I think we can only get better.”
Kane was one of seven changes made for the FA Cup tie, with Leicester making a swift return to White Hart Lane for a Barclays Premier League meeting on Wednesday night.