The past three matches between the sides had finished 4-0 in favour of Spurs and Mauricio Pochettino could not have wished for more accommodating opponents as his team won for the first time in five Premier League matches.
Ryan Shawcross' unfortunate own goal – the Stoke captain's sixth in the top flight – punctuated an uneventful first half but the wheels came off in worrying fashion for City boss Mark Hughes after the interval.
Kane had already passed up a pair of glorious chances by the time the excellent Son Heung-min made it 2-0 and the England striker's double made it three goals in the space of 12 second-half minutes.
Christian Eriksen got in on the act as Stoke's defence unravelled terribly, with Shawcross heading into the intended net 10 minutes from the end offering meagre consolation.
Spurs are up to fifth, above Arsenal and Burnley on goal difference, while Stoke and their battered goal difference sit precariously three points above the relegation zone.
131 - Only Alan Shearer (113) has reached 90 Premier League goals in fewer matches than Harry Kane (131). Chase. pic.twitter.com/bBpBtdfiQT— OptaJoe (@OptaJoe) December 9, 2017
The game was low on goalmouth action during the opening stages and there was a significant slice of fortune when Tottenham hit the front after 21 minutes.
Son had provided most of Spurs' attacking spark by that stage and the South Korea international made his latest dart for the byline down the left flank and whipped in a low cross.
His delivery flicked up off Kurt Zouma and Shawcross could do little as the ball struck him in the chest and zipped past goalkeeper Jack Butland.
Wembley was waiting for the net to bulge when Son threaded a pass through to Kane, played on-side by Stoke youngster Tom Edwards, but the striker uncharacteristically slotted wide.
Unperturbed by his earlier setback, Shawcross got in the way at close quarters to deny Kane with a pair of blocks two minutes before half-time.
6 - Ryan Shawcross has now scored six own goals in the Premier League; only Richard Dunne (10), Jamie Carragher (7) and Martin Skrtel (7) have scored more in the competition. Misdirected. pic.twitter.com/bfVGj2T88H— OptaJoe (@OptaJoe) December 9, 2017
Kane was still struggling to locate his usual poise early in the second period when Stoke failed to clear a corner and he hacked wildly over from four yards.
It fell to Son to show him how it was done in the 53rd minute, scampering on to Dele Alli's throughball and smashing past Butland after Harry Winks' flicked pass on the turn launched a Tottenham counter-attack.
Stoke were rattled and Butland scrambled behind having ceded possession to Kane before the Spurs striker finally got on the scoresheet 90 seconds after Son's goal.
Ben Davies was given far too much space to hang up an inviting cross to the back post, where Tottenham's top scorer leapt to power home.
There was a rare moment of encouragement for Stoke when Xherdan Shaqiri burst into the Tottenham box and forced a stunning reaction save from Hugo Lloris – Eric Dier turning the rebound just the right side of his own post.
Lloris' opposite number Butland was increasingly exposed and Edwards was found wanting when Son stole in front of him and laid off for Kane to sweep home with a sense of inevitability.
Erik Lamela then replaced Alli for his first Tottenham home game on the other side of his 13-month injury ordeal and Wembley was willing the ball into the net when he lunged in to try beat Butland from close range.
Hughes is unlikely to be the recipient of similar goodwill back in Stoke after this latest thumping, compounded when Eriksen breezed beyond a vacant backline to gleefully accept Son's fine 74th-minute pass, even allowing for the quirk of Shawcross bookending the scoring.
There was still time for Butland to wonderfully deny Eriksen, leading to the uncomfortable conclusion that Stoke's best player in a 5-1 hammering had been their goalkeeper.
Key Opta stats:
- Tottenham have become the first team in top-flight history to win four consecutive games against the same opponent by four or more goals.
- This was Stoke's 1,000th top-flight defeat, making them the 15th side to reach that figure since its inception in 1888-89.
- Harry Kane has scored eight Premier League goals against Stoke, only against Leicester City has he scored more in the competition (9).
- Ryan Shawcross is the first Stoke player to score at both ends in a Premier League game.