After narrowly missing out to Leicester for the league title last season, Spurs are now the closest challengers to Chelsea - albeit 10 points adrift of Antonio Conte's side.
Questions will be asked about Joel Robles, but that's not Harry's fault.
Tottenham, which is second on the table and 10 points behind Chelsea with 12 games remaining, hosts seventh-placed Everton on Sunday.
There was victory for their team, both got on the scoresheet and Kane moved clear at the top of the Premier League top scorer charts.
It would go down as Tottenham's ninth straight Premier League win on their own turf.
Within seconds of the handshake being beamed to a global audience of millions, many football fans with access to Twitter accounts let it be known how utterly appalled they were.
"Every day we push each other to be as good as we can be and that can only be good for Tottenham".
Everton manager Ronald Koeman has backed Chelsea to be "too strong" for their rivals during the Premier League the run-in. "Lukaku just can't find any space", said Smith in the first half.
Barkley featured for Everton in the Premier League match against Tottenham away from home at White Hart Lane in North London.
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The game had gurgled on for 20 minutes, as a congested Everton midfield made it hard for the hosts to carve out any meaningful chances.
"All round it was a good performance from us".
"If you compare the two teams of this afternoon its the third season of Pochettino at Tottenham".
I don't think we'll see Poch make any changes in the middle so Mousa Dembele should once again start alongside Victor Wanyama this weekend.
Lukaku, by contrast, was forced to drop deep in order to get the ball, giving him few chances to stretch Tottenham's backline until the closing stages.
For Mauricio Pocchetino's Spurs, the key trio of Jan Vertonghen, Toby Alderweireld and Harry Kane are all recovering from injuries and face late fitness tests before the game.
"Possibly it's a mentality issue", Liverpool midfielder Adam Lallana said, "and something that we need to learn quickly because time will eventually run out". "They try to do high pressing, and we like to".
"If you want to become one of the best world players if you look at the likes of Messi, Ronaldo, Thierry Henry they were players who were constantly improving, constantly getting better", Lukaku said.