However, it never looked liked David Wagner's men would make it three as Mauricio Pochettino's Spurs eased to a routine victory.
South Korean Son opened the scoring in the 27th minute after a pass from Dele Alli freed the forward to race clear and round Jonas Lossl before finishing low just inside the far-right post.
And then in the 54th minute the result was confirmed when Harry Kane whipped a sumptuous cross that Son ran onto to meet with a well-timed header at the back post.
Have a look below at some of the best lines from across the media on the Wembley Stadium encounter...
Spurs found the perfect opponents to help them prepare for the Champions League visit of Juventus next week. Please don’t misunderstand that. It is not meant to convey the impression that Huddersfield resemble Juventus too closely in any way. They do not play a similar style or pose a similar threat. They are, sadly for Huddersfield, hardly doppelgangers.
It is just David Wagner’s relegation-threatened side did very little to extend Tottenham before the biggest match of their season at Wembley on Wednesday. This was the kind of football-as-siege type of game that we have seen so often in matches between sides at opposite ends of the table this season. The phrase ‘routine victory’ was made for it.
The only surprise, really, was that Harry Kane did not score and join Alan Shearer and Thierry Henry as the only players in Premier League history to have scored 25 league goals in three consecutive seasons. That landmark can wait. It will come soon enough. As soon as the match was over, Spurs boss Mauricio Pochettino turned his thoughts to the second leg tie with Juventus.
It was hard not to imagine what Wembley will be like on Wednesday evening for one of the most pivotal games of the Mauricio Pochettino era while in the meantime, Tottenham Hotspur picked off their Premier League opposition with assurance of a side who knew bigger challenges lie ahead.
Their Champions League second leg round of 16 tie against Juventus next week is the test that you feel could define Pochettino’s season – at a stadium they have not lost in since August against a club that has made two of the last three finals in the competition.
By the end of this game against Huddersfield, Pochettino was able to substitute his goalscorer, Heung-min Son, yet another one of his match-winners who have taken the club into Europe’s elite.
Huddersfield have two critical home games coming up against Swansea City and Crystal Palace and Wagner suggested that their minds had always been on them first. At the end of the game the margin from Everton in 10th to Stoke City in 19th was just seven points and, three points clear of the relegation zone, Huddersfield may well survive.
A goal from Son Heung-min in each half was the bare minimum the hosts deserved from their 17th consecutive match unbeaten. It was not a lead they ever looked like giving up either, even at 1-0, as attacking prowess was matched by defensive power.
Huddersfield, for their part, were far too meek, clearly struggling to believe they could get anything from the game. Such an assumption was probably correct but it does not reflect well on David Wagner’s men. Their submission was certainly a compliment to Tottenham, however, and shows that Wembley is no longer an advantage for away teams.
The objective for Tottenham on Saturday was simple enough: to keep their Premier League campaign pointing towards a top-four finish and not to let their eyes drift towards the radiant glow of next Wednesday's Champions League's tie with Juventus. No muscle tweaks, no sloppiness, no complacency.
David Wagner's Huddersfield are having a contradictory season. On the one hand, the league table shows this season to have been a success. They were an unlikely playoff champion in 2017 and this year has seen them tussle admirably in a much higher weight class. They've quite rightly earned plenty of goodwill, not least for upending Manchester United and, more recently, a superb win against West Bromwich Albion. The bottom-half is congested enough to create a false sense of security, but they arrived at Wembley with their head well above water.
From another perspective, though, they've often been seen for what they are at this level: losing games with minimal fuss and, occasionally, with an all to meek approach. Conveniently, none of their results better exemplify that than the reverse of this fixture. Back in September Spurs cantered to a 4-0 win, playing expressive and penetrative football, but never having to leave second gear to do so.
To give Huddersfield their due, they weren't entirely passive. Shortly before Son made the game safe, Tom Ince drew a fine parry from Hugo Lloris and, a couple of times, a better touch at certain moments might have led to further opportunies. Nevertheless, there was never the slightest suggestion that they would leave Wembley with anything tangible.
This was a dominant performance in which Spurs played expansive, fast, fluent football from beginning to end. The front four of Son Heung-min, Dele Alli, Christian Eriksen and Harry Kane showed all their usual trust and understanding of each other’s games and, with a bit more luck in the box, Spurs would have scored five or six.
What made it even easier for Tottenham was that Huddersfield did not just want to park the bus and make things difficult for Spurs. They tried to press and play high up the pitch, which was admirable enough but when Alli and Kane both nearly scored in the first few minutes it should have been clear they were taking a big risk.