Kane struck twice in Spurs' 4-0 win in this fixture last season and although Mauricio Pochettino's side could not match that result on Saturday, the striker's first-half double was enough to seal victory.
Spurs were without Christian Eriksen, Dele Alli and Hugo Lloris due to injury, but Kane stepped up with a header and a penalty to follow his spot-kick in a 2-1 win at Brighton and Hove Albion in their last league fixture.
Huddersfield are bottom of the table with David Wagner's men still waiting for their first home league goal of the season, while Spurs move up to fourth.
Kane charged through on goal for the game's first big chance in the 10th minute, but Jonas Lossl was quickly off his line to smother the England captain's attempted chip.
Huddersfield were regularly exposed by long balls from the back and another led to the opening goal, Kane profiting with a header after Lucas Moura fed Kieran Trippier to cross.
Tottenham goalkeeper Paulo Gazzaniga had to make a fine save low to his left to push away a long-range Chris Lowe drive that swerved dramatically, but Spurs quickly doubled their lead.
Danny Rose went down under a challenge from Florent Hadergjonaj and Kane duly sent Lossl the wrong way from the penalty spot, with Laurent Depoitre unlucky to see a superb volley crash back off the crossbar as Huddersfield sought a response before the break.
Pochettino withdrew Jan Vertonghen and Mousa Dembele at half-time, with an eye on Barca, and Lucas had Spurs' best chance to extend their lead, the Brazilian blazing over the crossbar in the 64th minute.
What does it mean: Town look increasingly doomed
It is early to be writing teams off and facing Tottenham at home is not the kind of fixture the Terriers need to win if they are to stay up. But no home goals in six Premier League games, a dry spell that includes the end of last season, makes it clear where their problems lie. Defender Terence Kongolo being taken off on a stretcher in the first half only deepens Wagner's woes. Tottenham did not play particularly well but cruised to the points without needing to get out of first gear.
Kane delivers again for Spurs
A couple of weeks ago all the talk was about whether Kane was burnt out or merely temporarily jaded. But he has hit three goals in his last two Premier League games to quieten those critics, with Pochettino's decision to rest him in this week's EFL Cup tie against Watford a wise one. Without Alli and Eriksen, Spurs needed Kane to come up with the goods - and he did.
Dier struggles in dual role
Eric Dier has had a tricky start to the season and he was below-par again - it is tempting to wonder if his versatility is now counting against him. The England international played the first half in midfield and the second in defence after Vertonghen, who appeared to be struggling with injury, was replaced at the break. It may help Dier if Pochettino picked a position for him and stuck to it.
Key Opta facts
4 - Harry Kane is now the top scorer at the John Smith's Stadium in the Premier League with four goals in two appearances. Homely. pic.twitter.com/89KLpoHLJc— OptaJoe (@OptaJoe) September 29, 2018
- Huddersfield have failed to score in all four of their Premier League home matches this season. Only twice in top-flight history has a team failed to score in their opening five home matches of a season (West Brom in 1921-22 and Everton in 1998-99 – both five games).
- Tottenham have lost just two of their last 15 Premier League away games, winning 10 of those matches.
- Tottenham are unbeaten in each of their last eight games in all competitions against Huddersfield.
- Huddersfield have failed to win any of their first seven league games in a single campaign for the first time since 1997-98.
- Tottenham have scored in 32 of their last 33 Premier League games, failing to net only at West Brom back in May.
- He also became Tottenham’s fifth highest scorer of all time, having bagged 145 goals in 221 appearances for the Lilywhites.
- Since the start of last season, no player has provided more Premier League assists for another player than Spurs’ Trippier has for Kane (seven).