The striker took full advantage of a day to forget for Cherries goalkeeper Artur Boruc, scoring from the spot after being brought down by the stopper and adding two more to his tally in the second period - his third a deadly close-range finish after Boruc spilled the ball at his feet.
Mousa Dembele and Erik Lamela were also on target in the first half as we surged into a 3-1 lead after Matt Ritchie fired the hosts ahead inside 60 seconds.
It was the ideal tonic after a disappointing Europa League defeat in Anderlecht in midweek as, while the clocks going back has connotations of dark evenings and wintry weather, the sun shone brightly on the south coast, offering up perfect conditions for football.
There was just one change from our last Premier League outing with Eric Dier returning from suspension in place of the injured Nacer Chadli, with Dembele move further forward into attacking midfield.
It was the first time we had played Bournemouth in the league, but it was a nightmare start as we went behind inside the first minute.
A cross from the left by former Spurs man Charlie Daniels was collected by Ritchie, lurking at the back post, who kept his cool and fired a low shot into the bottom corner.
The home side had the momentum as we failed to get a foothold in the opening exchanges but we didn’t have to wait long for a leveller as Kane grabbed his second goal of the season from the penalty spot with nine minutes gone.
Christian Eriksen showed brilliant skill on the left to lose his man and slipped in a perfectly-weighted through ball for the striker, who was clattered by Boruc as he rushed off his line. The penalty was given and Kane dusted himself down to roll the ball home from the spot.
The goal gave us the kick-start we needed as we began to retain possession better and looked more of a threat going forward.
The second goal soon followed as a quick free-kick saw Danny Rose take aim from distance. His shot was blocked but fell kindly into the path of Dembele, who kept his cool to step clear of the Cherries’ defence and slot past Boruc.
We started to take control and almost extended our lead midway through the half but Boruc did well to palm away a Toby Alderweireld header from an Eriksen corner.
The home side looked dangerous down the flanks but were leaving the door open at the back and we took advantage to make it 3-1 just before the half-hour mark.
Kane was finding room down the left and he wriggled into space before sending a cross over that nicked off a defender. Boruc couldn't hold it and Lamela showed good anticipation to turn the loose ball into the net.
It was one-way traffic by then with the majority of the match being played out inside the Bournemouth half, but there was nearly a twist when Marc Pugh had a shot headed off the line by Alderweireld with Joshua King rattling the woodwork in the aftermath.
The hosts looked bright and breezy at the start of the second half and pressed us higher up the pitch.
Chances were at more of a premium than the first period but an opportunity came our way 11 minutes in and Kane buried it to make it 4-1, as he and Eriksen combined again to devastating effect. This time the Dane stepped in from the left and whipped a deadly ball in behind the Cherries’ back line that Kane steered past Boruc with one movement.
Harry looked intent on taking home the match ball and but for a good save from Boruc three minutes later would have secured his hat-trick following good work from Kyle Walker.
He would not have to wait much longer, though, as from the resulting corner, Boruc again fumbled – this time from an Alderweireld header – and there was Kane to prod home from a couple of yards out for his simplest finish of the afternoon.
Eriksen almost made it six when he let fly from 30 yards but his effort rattled the post with Boruc beaten.
Ryan Mason came on for Dembele for his first appearance since picking up a knee injury at Sunderland in mid-September, while Kane wanted another penalty with 20 minutes to go as Boruc this time fumbled a Dier cross and appeared to upend the striker inside the six-yard box.
The referee waved play on, though, with our next change seeing the introduction of right-back Kieran Trippier for his first Premier League appearance in our colours in place of Walker.
Clinton Njie followed him off the bench, replacing man of the moment Kane, and was quickly into action, racing through down the left channel - only to see his eventual shot turned around the near post by Boruc.
It was plain sailing in the closing minutes, with only a Simon Francis cross from the right - hacked away by Jan Vertonghen - of note as we returned to winning ways in style.
AFC Bournemouth (4-2-3-1): Boruc; Francis, Cook, Distin, Danies; Surman, Gosling; Ritchie, King (O’Kane 61), Pugh (Smith 75); Murray (Kermogant 67). Substitutes (not used): Federici, Rantie, Stanislas, Bennett.
Spurs (4-2-3-1): Lloris (c), Walker (Trippier 82), Vertonghen, Alderweireld, Rose; Dier, Dembele (Mason 67), Alli, Eriksen, Lamela; Kane (Clinton 85). Substitutes (not used): Vorm, Wimmer, Onomah, Townsend.
Goals: Bournemouth – Ritchie 1. Tottenham – Kane 9 (pen), 56, 63. Dembele 17, Lamela 29.
Yellow cards: Tottenham – Rose 31.
Referee: Roger East.