The 23-year-old has now registered 26 times for Spurs in the Premier League this term and 32 times in total, making this the third season in a row that he has passed the 30-goal mark - although last year's tally of 32 included four England goals.
Shakespeare also challenged his players to make amends by ending the season with victory over Bournemouth, which would allow them to finish in the top half of the table.
Only 26 players in Premier League history have reached 100 goals.
Tottenham Hotspur can not compete with their Premier League rivals offering huge wages in the transfer market despite securing a Champions League berth for the upcoming season, manager Mauricio Pochettino has said.
The England global is in line to collect his second Golden Boot in a row and is only the fifth player since the Premier League began to score 25 or more goals in successive seasons, following in the footsteps of Robbie Fowler, Thierry Henry, Alan Shearer and Robin van Persie.
While it is true that Tottenham are building a new stadium, the club are very much capable of saying "no" if Premier League rivals want to sign their top players. This game means nothing to either side but it will be the last time Hull City see Premier League action in a while and I do not think that the home fans will want to leave the Premier League with a loss.More news: Judge rules no discrimination, then sends him off with empty pockets
Alexis Sanchez has taken the most shots of the three Golden Boot contenders. Kane snares his second of the game with a simple header from close range after Wanyama had nodded Alderweireld's hanging cross back into the danger zone.
Van Persie was the last player to win the Golden Boot in consecutive seasons when he did so in 2011-12 and 2012-13. He left it two goals ahead after putting four past the Foxes in a 6-1 demolition.
Harri-kane wrecked Leicester City. "I was looking to get one or two goals at least and then hopefully take it into the last game, now I'm in the driving seat at the minute but there's still one game to play so I'm not resting on my laurels".
"It was probably one of the best performances of the season".
With Everton travelling to Arsenal on the final day of the season, the odds are massively in Kane's favour to win his second Golden Boot in successive seasons.
Harry Kane scored four times as Tottenham produced another superb performance to sweep aside Leicester City.