With a third of the season gone in the English Premier League, they are within two points of Arsenal in fourth and four behind surprise leaders Leicester.
No one typifies the spirit of Mauricio Pochettino's side better than Kane: brimming with freshness, energy and desire, without the pretension of those who think it ought to be done differently, or more prettily, perhaps.
But it goes deeper than the striker who has emerged to spearhead the Pochettino revolution and save Daniel Levy a small fortune.
This Spurs team has a solid bedrock. It feels durable.
Hence the optimism that this new dawn is not false. Not like all the others.
Hugo Lloris is a modern and adventurous goalkeeper, and three strong and physically imposing defenders: two Belgian centre halves (one of whom just happened to find the net against West Ham) and Eric Dier, the midfield anchor.
Jan Vertonghen has been transformed from rampant but unreliable Super-Jan into the dependable rock at the back. Toby Alderweireld beside him has been a positive influence. When Vertonghen smothered Andy Carroll and drove the West Ham centre forward into touch in the final seconds of the first half, there were high-fives among Tottenham's entire defensive unit and they made their way off the pitch.
The clean sheet was intact, as it would be until Lloris was beaten by Manuel Lanzini's brilliant strike, but Spurs had performed well throughout the second half, refusing to relax their tempo because the game was won once the third went in.
Still they chased and hassled. Pochettino deserves credit for instilling this mood and imposing the base fitness levels which have become legend. Out went the various dissenting figures, while those prepared to commit to his philosophy have thrived.
Dele Alli was at the heart of everything, having been pushed forward into the space behind Kane, where he finished the game at Arsenal.
The pair were a nightmare for West Ham's back four, giving them no time to relax or catch breath, while always threatening the goal.
Spurs are moving on up: good to watch and developing fast.
And this time it might be different.
- Daily Mail