Scintillating Spurs are now just two points behind second-placed Manchester City and trail Liverpool by six but after this performance, the London club look well capable of pushing their rivals all the way.
"Everybody's been talking about Liverpool and Manchester City, and we've been getting on with it and doing well, like we normally do," said Kane.
"We've had a good month and hopefully we can take that into January now - and February - and we'll see where we're at come April time."
Media speculation has suggested Spurs manager Mauricio Pochettino could be a target for Manchester United at the end of the season, but if the Argentine had any doubts about the potential of the side he has created they would have vanished with this display.
Despite falling a goal behind, Spurs were simply unstoppable once Son had brought them level in the 27th minute, with their devastating movement in attack and precision passing from midfield too much for an Everton side whose limitations were ruthlessly exposed.
Everton took the lead in the 21st minute when Dominic Calvert-Lewin pulled the ball back to former Arsenal forward Theo Walcott who turned it past Hugo Lloris.
After Calvert-Lewin had a header harshly ruled out, Spurs drew level from an awful mix-up between Everton keeper Jordan Pickford and defender Kurt Zouma with South Korean Son doing well from a tight angle to curl the ball into the unguarded goal.
That error changed the game and Spurs never looked back as their flowing, attacking football, a joy to watch, overwhelmed Marco Silva's side.
Spurs went in front in the 35th minute when Dele Alli drilled home the ball after Son's shot was parried by Pickford.
Three minutes before the break, the visitors made it 3-1 when a Kieran Trippier free kick flew out off the post straight to Kane who gleefully converted.
Christian Eriksen made it 4-1 in the 48th minute when Kane's shot was blocked by Seamus Coleman and the Dane showed great technique as he drove the ball past Pickford from 20 metres out.
Everton responded though, three minutes later, with Gylfi Sigurdsson cutting across the edge of the area and reversing a shot into the bottom corner.
Any hope of an Everton revival was short-lived as substitute Erik Lamela slipped in the superb Son who confidently drove past Pickford to make it 5-2.
The irrepressible Son then created the sixth, with his perfectly delivered cross from the left met with a textbook finish by the sliding Kane.
Such was the quality of Son's display that parts of the Everton crowd joined in with the visiting fans to applaud him off the field.
The South Korean had tormented Everton throughout but the entire Spurs team had shown that they are certainly more than also-rans in the title race.
City's loss to Crystal Palace on Saturday allowed Liverpool to take command with a four-point lead at the top but it also opened the door to a Spurs team who have marched through it in such emphatic fashion.