But Tottenham stormed back through two Erik Lamela efforts and an unfortunate Christian Fuchs own goal before Vardy equalised, only for Kane to settle matters by curling home his 30th league goal of the campaign.
Tottenham Hotspur manager Mauricio Pochettino called on the club's chairman Daniel Levy to match his ambitions by being "brave" in the transfer market ahead of moving to a new 62,000 capacity stadium.
Spurs ended the season with a freakish 5-4 home victory over Leicester that secured them a third-place finish, though their points total of 77 was nine short of their 2016/17 finish - and 23 points behind champions City.
Pochettino wants at least £100m to reinvigorate Tottenham's squad.
"You need to be courageous in this kind of situation, in our club with our unbelievable fans, and take risks".
"I think Daniel is going to listen to me". But you know me and sometimes I have some insane ideas. "Being in that senior working environment every day can only help you to get better and I think when I've been given my opportunities, I've been able to show my improvement and help the team to win games", Peters added. We need to work harder than the previous season to be competitive again.
Pochettino's future at Spurs is now uncertain, and Merson feels that Real Madrid will target him to replace Zinedine Zidane, if they fail to win the Champions League final.
Levy operates a strict wage structure at Tottenham with the club's salary budget dwarfed by their top-six rivals.
Pochettino has been widely praised for breaking into the top four on a consistent basis, but insists much more needs to be done if he is to lift his first trophy as a coach next season.
"He's a goalscorer and of course it's a good feeling to finish with 20 goals with his quality, and I hope in the future we can continue to give him good service and he can score a lot of goals". I think I have very clear ideas of what we need to do.
"That's up to Daniel and the club".
"If we want to be real contenders for big, big trophies, we need to review a little", Pochettino said.
"You can not create dreams thinking you are not going to achieve these dreams".
Spurs will no doubt be disappointed to lose the 29-year-old but the Evening Standard claims they will use the money raised from his sale to launch a swoop for highly-rated Ajax star de Ligt.
And it is understood the contract dispute is causing friction to his relationship with the club.
The Blues will now try to end the season on a high when they take on Manchester United in the FA Cup final at Wembley on Saturday evening. This time, he was more direct, essentially demanding signings. I think it was a insane game. "But tomorrow I don't know what is going to happen". It's not important. The most important thing is what the club thinks, not you or the speculation about me.