Kane moved clear at the top of the Premier League scoring charts as he put the hosts into a commanding two-goal lead in the opening 15 minutes at White Hart Lane, before Christian Eriksen added a third just after half-time.
And they got just that when Kane, who netted a hat-trick in the 5-1 win at the Vitality Stadium in October, drilled home with just 43 seconds on the clock, before doubling his tally with another exquisite finish after being played in brilliantly by Dele Alli.
Bournemouth came out fighting in the second half, but the result was swiftly put beyond all doubt as Eriksen capitalised on an error from Artur Boruc to tap-in from close range and condemn Eddie Howe's side to their first defeat on the road in 2016.
Bournemouth had taken the lead in the first minute in the reverse fixture, but it was Tottenham who struck first on this occasion when Kane turned home Kyle Walker's superb cross.
That strike took Kane to the top of the top-flight scoring charts, and the England striker did not have to wait much longer to rack up a 21st goal of the season as he spun in-behind Bournemouth's defence to race onto Alli's pass and dispatch a low strike past Boruc.
Pochettino's side believed they had got a third when Alli drove home on the half-volley from close-range, but the strike was disallowed as Kane had strayed offside in the build-up.
Steve Cook headed just over the crossbar as Bournemouth finally managed a meaningful attack shortly before the interval, while Eriksen could not stretch far enough to tuck home from Kane's cross-cum-shot at the other end.
Despite some promising play from the visitors, Tottenham finally got their third seven minutes after the interval as Boruc spilled Kane's dipping, long-range strike straight into the path of Eriksen, who duly nudged home.
Alli would have put further gloss on another fine individual display had he not skewed a gilt-edged chance wide, before Kane went close to a hat-trick late on with a rasping drive from 25 yards as Spurs pressed home dominance which saw Bournemouth fail to register a shot on target.