Kane got us off the mark early on with a fine curling finish and after Christian Eriksen hit the bar, our second goal arrived through Dele Alli's deft flick midway through the second half.
Alli then missed a sitter but his blushes were spared by Kane as he grabbed the third moments later, with Alli eventually getting his second to inflict the Potters' joint-heaviest home defeat in the Premier League era and our biggest win against them since October, 1984.
Indeed, just minutes after Leicester’s result on Sunday, Kane posted a photo of a hungry-looking pack of lions on his Instagram page. The message was clear; we mean business, and boy did we show it with a complete performance at the Britannia Stadium.
Actions of course speak louder than any post on social media and the intensity and quality of our performance in an emphatic win showed the team's staying power in the run-in to the end of the season.
Mauricio Pochettino kept faith in the same XI that put Manchester United to the sword last weekend while our supporters were in fine voice early on. They almost had a goal to cheer about six minutes in as Kane took possession inside the box but the striker just got the ball stuck under his feet and Shay Given - making his league debut in goal for Stoke - comfortably dealt with his effort.
Kane more than made amends three minutes later, though, when he broke the deadlock in style. Mousa Dembele laid the ball off to the England forward on the corner of the box and, with seemingly little options, the striker shifted it on to his right foot before whipping a wonderful finish beyond Given into the bottom corner.
Few could say our lead wasn’t deserved as we dominated the early exchanges with the home side struggling to get a foothold in the game.
The tide started to turn as the half wore on as first Marko Arnautovic tested Hugo Lloris with a snapshot on 27 minutes before he glanced a header wide a minute later.
A series of corners followed as the home side enjoyed the first spell of sustained pressure. We stayed strong, though, and Dembele let fly from 30 yards, narrowly missing the top corner.
We continued to look a threat on the counter with Kyle Walker finding acres of room to gallop into on the right-hand side on more than one occasion, although we couldn't take advantage.
We should have extended our lead with five minutes of the half remaining when Alli delightfully flicked into the path of Eriksen who had only the goalkeeper to beat, but he rattled the bar with his effort from a central position.
The home side were far less sluggish out of the blocks for the second period and put us under some early pressure with Ibrahim Afellay firing a dangerous shot across the face of goal.
Danny Rose then had a glorious chance to stretch our lead when he raced through on goal from a perfect Kane through ball but, under pressure from Philipp Wollscheid, he lost his footing as he tried to round Given.
Next to go close was Alli from the edge of the box after Eriksen trapped a ball into his path but still the second goal evaded us. Lamela brought the best out of Given with a rasping shot just before the hour mark following a dangerous cross from Walker.
We were back in control and creating chances galore as we countered and cut through the home side at will - it was only our finishing that was lacking. Toby Aldrweireld had a shout for a penalty denied when he was hauled down by Ryan Shawcross from a corner.
Finally the second goal came through that man Alli, but the credit must go in part to Eriksen for the assist. The Dane picked Alli out with a glorious first-time pass and the youngster kept his cool to control the ball and flick delicately over Given on 67 minutes.
Moments later, though, he would have wanted the ground to swallow him up. Released by Kane, he rounded the goalkeeper and, with an open goal to aim at, he struck the post.
It was all over on 71 minutes when Lamela beat the offside trap and squared for Kane to tap home his second of the game.
The fourth goal arrived on 82 minutes as Eriksen surged into the Stoke box down the left and crossed for Alli, who opened his body and found the bottom corner with a right-footed volley.
Substitute Nacer Chadli tried to get in on the act when he bustled his way down the left before pulling the trigger, but his effort flew just over.
Joselu had the last chance of the game for Stoke, steering the ball towards goal, but Lloris was equal to it.
The result means we've now scored 13 goals and conceded only once in our last five domestic games.
Stoke City (4-2-3-1): Given; Cameron, Shawcross (c), Wollscheid, Muniesa; Whelan (Adam 76), Imbula; Shaqiri (Joselu 46), Afellay, Arnautovic; Bojan. Substitutes (not used): Haugaard, Bardsley, Ireland, Diouf, Crouch.
Spurs (4-2-3-1): Lloris (c); Walker, Alderweireld, Vertonghen, Rose; Dembele (Mason 87), Dier; Lamela (Son 90), Eriksen, Alli (Chadli 84); Kane. Substitutes (not used): Vorm, Davies, Trippier, Wimmer.
Goals: Spurs – Kane 9, 71, Alli 67, 82.
Yellow cards: Stoke – Imbula 61, Adam 80.
Referee: Neil Swarbrick.