The England captain struck twice in the first half to ensure it was another frustrating day at the John Smith’s Stadium for David Wagner’s men.
Laurent Depoitre struck the crossbar, while only a fine save from Paulo Gazzaniga prevented Isaac Mbenza snatching a late goal for Town.
This latest blank means the current crop have now matched an unwanted record of six home games in a row without a goal.
That came in the 1971-72 season that ended in Huddersfield being relegated and unless Wagner’s men improve their goal output very, very soon then this campaign is heading in a similar direction.
Kane’s first goal came in the 25th minute via a swift break. Terence Kongolo was able to halt the rampaging Spurs attack with a slide tackle on Lucas Moura.
But the simply got to his feet and rolled a pass to Trippier, whose cross was headed in by Kane. Kongolo was then stretchered from the field, the first of two Terriers defenders to be forced out of the action with Christopher Schindler limping off in the second half.
Chris Lowe came mightily close to equalising with a drilled shot that Gazzaniga turned round the post but Spurs doubled their lead ten minutes before the break when Florent Haderjgonaj was adjudged to have tripped Danny Rose.
Kane did the rest from 12 yards to leave Huddersfield, who hit the crossbar through Laurent Depoitre in stoppage time.
The hosts kept going to the very end but could not breach the Spurs defence, Mbenza going closest with a dipping shot 11 minutes from time that Gazzaniga did well to keep out.
"There was such an incredible atmosphere in the stadium because the players left everything on the grass," said Town boss David Wagner.
"The guys did that without reward, but if we continue to create chances the rewards will come.
"You have to show desire and passion and you need a bit of luck, which we don't have at the moment."