Kane went into the game fresh off the back of his Champions League hat-trick in midweek and he looked full of confidence from the outset.
However, after an early flurry of corners for Spurs, Huddersfield actually looked to have had the better start.
Tommy Smith called Hugo Lloris into action with a powerful long-range effort, whilst Ben Davies and Eric Dier has to make last-ditch challenges to prevent the hosts from having a sight of goal.
That good work was undone after just nine minutes though as Kane continued his incredible run of form.
Jonas Lossl’s clearance was poor and when Kieran Trippier headed the ball on for Kane to race clear, the England international made no mistake, firing past the goalkeeper at his near post.
That goal came against the run of play but from that point on there only looked like being one winner.
Spurs doubled their lead just six minutes later, a beautiful team move involving Kane, Alli and Eriksen ended with the latter having the ball nicked off his toe by Schindler but it dropped perfectly for Davies to dink over Lossl and find the far corner.
The hosts had a half-hearted appeal for a penalty on the 20 minute mark when Kachunga went down under the challenge of Davinson Sanchez but referee Neil Swarbrick waved away their protests.
Lossl almost gifted Kane a second second later as he missed his clearance but the ‘keeper was able to recover and smother Kane’s effort.
The 24-year-old wasn’t made to wait too long for his second of the afternoon though as after 24 minutes, he gathered a throw-in from the right, spun his man and fired into the far corner with his left foot from the edge of the box.
Dele Alli then struck the post as Spurs threatened to run riot, before Kane saw a goal rightly chalked off for offside. The striker had just strayed beyond the last man as he latched on to Davies’ cross from deep on the left as he went in search of his second hat-trick of the week.
Laurent Depoitre reminded Spurs that the ‘Terriers’ could still pose a threat just before half-time as he crashed an effort from range off the bar but the visitors went into the break very much in control.
Mauricio Pochettino’s side continued to control the game in the second half, despite never really getting out of second gear.
Huddersfield appeared to have been under orders from boss David Wagner to tighten up during the second 45 and to employ a damage limitation policy and they did exactly that.
Jan Vertonghen blasted over from range before Eriksen tested the eccentric Lossl with an effort from the edge of the box.
Huddersfield arguably had the best chance of the second period when Kachunga came within inches of heading home Scott Malone’s cross from the left after good work from Rajiv Van La Parra.
But it was Spurs who would have the final word when substitute Moussa Sissoko found the net in injury time with the aid of a big deflection of Schindler after a delightful cross from Davies.
The win was just the result Pochettino will have been looking for ahead of the international break, whilst David Wagner will be forced to admit that the visitors were just too good for his side.