Harry Kane continued his brilliant recent form with a double, Harry Winks impressed in midfield and the full-backs, Kieran Trippier and Ben Davies, notched three assists and a goal between them during another productive afternoon on the flanks.
There was even a goal for Moussa Sissoko, his first in 44 Premier League appearances for Spurs. The only worrying thing for Pochettino was Real Madrid transfer target Dele Alli's dive when his side were already 3-0 ahead. But, by and large, it was a stellar team performance, with the defence once again shining to keep a fourth clean sheet this season.
The Colombia international, still only 21, has impressed following his arrival from Ajax in the summer and is already confidently answering any questions over whether he was a worthwhile investment at a club record £42million.
Sánchez The Student
With the manner in which Sánchez has acquitted himself in the Premier League, it would be easy to conclude that he has been a defender his whole life.
In fact, when he signed for Colombian side Nacional in 2012, he was an aggressive midfielder but, thanks to the excellent man-management skills of his coach, Felipe Merino, he learned to develop both the mental and physical side of his game as a central defender.
That transformation led to Sánchez becoming a key figure in Nacional's triumphant 2016 Copa Libertadores campaign. Naturally, there was interest from Europe and, desoute Barcelona transfer rumours, the player chose Ajax because he felt there would be more first-team opportunities in Amsterdam.
He wasn't wrong. Sánchez made 43 appearances in all competitions for Peter Bosz's side as they reached the Europa League final, capturing the imaginations of many footballing purists that longed to see Ajax return to the forefront of the game once again.
Although the club's season ultimately ended in disappointment, both domestically and in Europe, Sánchez established himself as one of the brightest defensive prospects in Europe.
He was named Ajax's Player of the Year and when Spurs came calling, Sánchez readied himself for another huge step up in his fledgling career. In around 18 months, he had gone from breaking into Nacional's team to facing Manchester United in a European final to becoming Tottenham's all-time record signing.
In just two months, Sánchez has made already impressive strides to justify his hefty price tag. Playing as the deep anchor in Tottenham's back three, Sánchez offers excellent tactical discipline, pace and aggression.
With an average of 5.4 clearances per game, according to WhoScored, Sánchez is outperforming both Vertonghen (4) and Alderweireld (4.3), while his 58 per cent win average in the aerial duels department is also the highest in the Spurs team.
What has marked Sánchez out already is his intuition when it comes to where to position himself on the pitch. There is an ongoing narrative in modern football that, with the rise of the ‘ball-playing centre-half,' some of defending's fundamental concepts – like positioning – have been demoted in importance.
Sánchez bucks that trend. His high clearance rate is a product of always being in the right place at the right time but, like his idol Franco Baresi, it's by design and not a coincidence.
Take Spurs' recent win over West Ham United as an example. Sánchez is switched on from the start. When the Hammers launch an attack, the Colombian knows exactly how to respond.
As Marko Arnautović runs forward, Sánchez assesses the situation while on the move. He has one look over his right shoulder and sees Michail Antonio. He points to Vertonghen to get tight. Having a second look, he sees that the Belgian has picked him up, enabling Sánchez to defend the near post.
Positioning himself six yards out from Hugo Lloris's goal, he has another quick look to see Javier Hernández making a late dash. As Arnautović's ball comes in, Sánchez is perfectly placed to make the interception and prevent Hernández, a skilled poacher, from surely tapping home.
Against Huddersfield, Sánchez demonstrated these characteristics again as he marked Laurent Depoitre out of the game. In the seventh minute, with the score still 0-0, Sánchez impressively outmuscled the Belgian striker to break down a promising Huddersfield attack.
When Tommy Smith plays the ball forward, it becomes a foot race between Sánchez and Depotire, one the Colombian defender wins before going to ground and making the tackle.
Sánchez's instinct to defend the space behind himself and Depoitre is one of his impressive traits. His thinking was to shut off the space between Depoitre and the goal. His positioning allowed him then to use his pace and aggression to win the battle.
There was simply no joy for Depoitre and Huddersfield on Saturday. Sánchez was an impenetrable presence at the back, making seven clearances, winning 100 per cent of his tackles and two aerial duels.
Pochettino Playing To His Strengths
Like with any young player, Sánchez has his weaknesses. When Manchester United beat Ajax in the Europa League final in May, José Mourinho said he had identified a weakness of Sánchez: playing out from the back. As this was a key tactic in Bosz's Ajax, Mourinho felt that he could hurt Ajax by blocking Matthijs de Ligt and forcing them to play out through the Colombian.
Former Ajax academy coach Wim Jonk added that he felt as though Sánchez also had to think faster if he was to succeed at Spurs, but Pochettino has used him adeptly and has cleverly shielded some of those perceived shortcomings.
Playing as the deepest of three centre-backs, Sánchez sits back and allows Vertonghen and Alderweireld to push slightly further up the pitch. The Belgian duo have played under Pochettino for longer and thus have a deeper knowledge of their manager's vision and requirements.
Pochettino feels as though Sánchez has the pace, mobility and reading of the game to operate as the anchor. If Vertonghen or Alderweireld are exposed, Sánchez has the attributes to get across on the cover.
And, while Mourinho's assessment may have been correct in May, the defender is quickly learning how to circulate and retain possession effectively. His pass completion rate this season is an impressive 93 per cent. Against Huddersfield, he completed 70 of 73 passes, more than any other player on the pitch. If having the ball at his feet was a weakness when he was at Ajax, he is certainly developing at a rapid rate under Pochettino.
The first screenshot below, per Squawka, shows Sánchez's wayward passing in the final against United. The second one shows his performance at Huddersfield.
Pochettino is a meticulous and thorough coach and will have been well aware of Sánchez's weaknesses before signing him. However, under him, Vertonghen and Alderweireld have established themselves as two of the most consistent defenders in the Premier League and, given time, there is no reason to suggest Sánchez can't do the same.
Real and United Tests Lie Ahead
Not to discredit his recent displays against APOEL Nicosia and Huddersfield, but Sánchez certainly has more robust examinations of his abilities at this level ahead. He hadn't signed in time to play in Spurs' defeat to Chelsea in August but performed solidly against Borussia Dortmund. Greater tests lie beyond the international break, though.
Tottenham's next six games include home and away Champions League games against Real Madrid, hosting Liverpool at Wembley and travelling to Old Trafford to face Manchester United. All of those games will serve as a barometer for the progress Sánchez has already made, while it will be intriguing to see if Mourinho tries to highlight the Colombian as a weakness in the Spurs ranks like he did when he was at Ajax.
With the prospect of facing Cristiano Ronaldo, Romelu Lukaku and Sadio Mané looming after the international break, Sánchez will need to be at his very best if Spurs are to extend their impressive eight-game unbeaten streak.
Being humbled at the hands of Ronaldo may damage his confidence briefly but, having been self-assured enough to reject Barcelona and play with a freedom at Spurs that belies his enormous transfer fee, there is no doubt that Sánchez possesses the mentality and character to simply focus on improving for the next game.
Of course, mark Ronaldo out of the game or shut down an in-form Lukaku, and expect to see plenty more glowing appraisals of Sánchez in the weeks and months to come.