With less than half an hour played, Kyle Naughton was red-carded for handball. West Ham's Mark Noble missed the subsequent penalty, but it forced a tactical change from Pochettino, who switched debutant Eric Dier to right-back (with Etienne Capoue moving back into central defence for him).
Andros Townsend replaced Aaron Lennon on the hour mark, and the substitution prompted more positivity from Tottenham—although the mood change was also aided by James Collins getting sent off for a second bookable offence shortly after.
Then, with two of four stoppage-time minutes having been played, another substitute—Harry Kane—played Dier in behind the Hammers defence. The new signing rounded goalkeeper Adrian and calmly shot into the back of the net. Cue jubilant scenes in the away end at Upton Park.
Those are the basic facts of the game. The prominence of the English involvement in them was testament to Pochettino's smart decision-making at crucial moments. But it was also because some of his original ideas did not come off on Saturday.
Naughton's dismissal came during a period of sustained West Ham pressure.
Spurs had started attractively, passing it nicely while Christian Eriksen and Erik Lamela looked to take on the opposition. But no real instinct to dominate the home side emerged—just a disconnect between the attack and those behind.
As was the case last May, Sam Allardyce's side took advantage of the room and time granted them by planting crosses and balls forward directly on the hesitant Spurs defence. Carlton Cole and Ricardo Vaz Te worked hard to get onto these deliveries, particularly by the impressive Stewart Downing (left-back Danny Rose defended well in his box but failed to get near the winger outside it), but lacked the bruising quality Andy Carroll posed last time out.
Naughton had been alert to stop Cole 10 minutes earlier, and it was unfortunate his continued awareness got him sent off. Having tracked Kevin Nolan, he blocked his shot with his outstretched arms. A definite penalty, but a harsh dismissal given how close he was to the shot.
Pochettino had the opportunity there to change things up throughout his team. Instead, the patience he exhibited in bravely sticking with his original strategical intent was admirable. He trusted in Capoue and Dier to adapt (which they both did well) and granted the team time to try and work things out further forward.
Ultimately, they would not in the team's original form. But nobody anticipated his plans to implement a more focused attacking style at Spurs would pay off perfectly straight away.
As the above statistics indicate, Tottenham had more joy getting at West Ham in the second half. This was in large part thanks to the galvanising introduction of Townsend.
The winger's breakthrough year of 2013 gave way to an early 2014 that was marred by injury problems and accusations of a one-track mind in the final third.
He still has work to do refining his talents here. But after Eriksen, Lamela and Lennon had struggled to create much of note, Townsend's directness was just what Spurs needed.
The 23-year-old fired in two dangerous shots within the space of two minutes shortly after coming on. Thereafter, he put West Ham on the backfoot with his dribbling and—helped by the better movement provided by fellow substitute Lewis Holtby—combined intelligently with his team-mates around the box.
The impetus regained, Pochettino's decision to bring Kane on in the final 10 minutes was a sensible one, too. Emmanuel Adebayor had been a disappointing presence up top for Spurs (save for winning the foul that got Collins sent off). Although he undoubtedly lacked good service for large parts of the game, his work rate was not good enough compared to Cole and Vaz Te down the other end.
As it was, Kane was wasteful in the first few times he saw the ball. But his assist for Dier was a real moment of class, showing movement and quickness of thought that Adebayor barely got close to all afternoon.
The finish was a real beauty from the makeshift right-back, too, as was the run in from the right. Dier had focused on defensive duties for the most part following Naughton's departure but had tested his legs with a powerful run down his flank four minutes before his goal. West Ham should have heeded the warning.
Dier's early struggles alongside Younes Kaboul will remind him work is to be done conditioning himself to more physically and directly inclined English attacks. But the expatriate recruit from Sporting Lisbon should be pleased with his first Premier League appearance.
As, too, should Pochettino with his first match proper managing Tottenham.
Had Noble converted his penalty kick, it might have been a different story. Spurs rode the storm, though, and took three points that, eventually, they were good for.
Day 1 of the 2014-15 Premier League season for Tottenham was about the contributions of the team's young Englishmen and the decisions to utilise them by their Argentinian boss. Moving forward, Pochettino will be working to get more from the rest of the nationalities in his squad.