Mousa Dembele and Heung-min Son put Mauricio Pochettino's side in control by the break with measured finishes as the Cherries struggled to get a foothold in the game.
Kane then confirmed his ankle injury is behind him with a powerful drive and Vincent Janssen wrapped up Spurs' record 12th consecutive home victory in stoppage time.
The north Londoners have dropped points in front of their own fans on just two occasions this term and appear destined to push Antonio Conte's side all the way during the run-in.
Dominating opponents at White Hart Lane has become routine and Spurs only needed a few minutes to find their rhythm.
Christian Eriksen's cross fell to the right man but Kane saw his bundled effort well saved by Artur Boruc before the linesman's flag was raised.
Dembele tested Boruc with a fierce drive from the edge of the area as Spurs began to turn the screw.
And the visitors' resistance was broken when the Belgian midfielder collected Toby Alderweireld's near-post flick on before rifling home from inside a crowded penalty area.
The Cherries struggled to cope with Spurs' determination to press from the front and were punished when Jack Wilshere, whose every touch led to a chorus of boos, was caught in possession.
The Arsenal man's loose touch fell to Kane, who picked out Son with a cute flick, and the South Korean produced an accomplished finish from a tight angle to take his tally to the campaign to 19.
Eriksen was twice unfortunate not to add another before the break, with Boruc bordering on becoming the busiest man on the pitch.
But Bournemouth dug in to keep the scoreline respectable - much to Mauricio Pochettino's frustration. The Argentine coach turned on his heels and headed straight down the tunnel, seemingly unsatisfied with his side's commanding display.
Such a relentless attitude yielded a third goal while Eddie Howe's team talk was stilling ringing in Bournemouth's ears as Kane shrugged off the attention of Simon Francis before slotting home.
Boruc needed to be alert to deny Kane and Eriksen with another goal seemingly a certainty but Pochettino had to settle for just three.
Spurs fans were enjoying another vintage display from their side and Wilshere's withdrawal due to a calf problem was greeted warmly.
Kane's afternoon also came to an end early, but out of luxury rather than necessity, allowing Janssen a chance to tap home at the death.
The striker - like Spurs - is primed to finish strongly. Over to you, Chelsea.