Pochettino had won just three of his first nine League games and was already feeling the pressure from chairman Daniel Levy when Kane came off the bench to score a last-gasp, deflected free-kick.
At Spurs, ‘the Villa game’ has become widely acknowledged as a sliding-doors moment in the club’s recent history, and the handful of senior players who were at the club then, including captain Hugo Lloris, have genuinely used the example this month as a reason to keep patience with Nuno.
Lloris and Kane, who scored a 19-minute hat-trick last night as Spurs thrashed NS Mura 5-1 in the Europa Conference League, in particular, are mindful of how long it took Pochettino to instil his philosophy and see parallels in Nuno’s own attempts to rebuild.
How Nuno could do with his own Villa moment at home on Sunday, after three consecutive defeats to London rivals have left him under intense pressure.
And as much as a result against Dean Smith’s in-form side, Nuno needs a successful game-plan after his disastrous tactics in the defeats to Crystal Palace and Arsenal.
The challenge for the Spurs manager has quickly become as much about style as substance, in part because he always looked a questionable fit for Levy’s desire to hire an attacking successor to Jose Mourinho and partly because Spurs have looked so dour in his six League games in charge.
Earlier this week, Nuno was asked if he was aware of ‘the Tottenham way’ and the style in which he is expected to play, reflecting the narrative around his stuttering tenure.
Spurs are not only under pressure to start winning but to do so in a more convincing and coherent way than the victories over Manchester City, Wolves and Watford at the start of the season.
Nuno has often appeared to be stuck between his own philosophy — a “solid” base and quick counter-punches — and the progressive style demanded by fans and the club, in stark contrast to Pochettino, who never lacked conviction in his approach.
Nuno struck on a promising formula in the first half of the 3-0 defeat to Chelsea before the quality of the European champions eventually told, but he abandoned the high-risk, high-pressing style in favour of a direct approach against Arsenal, characterised by an almost total absence of midfielders and in which his players appeared to have little faith.
Mourinho generally played conservative football last season but he could fall back on his reputation and some exhilarating early-season demolitions of Southampton and Manchester United, which appeared to prove he could play another way.
Nuno, though, has neither a haul of trophies nor recent evidence of attacking football, while he is also in the unfortunate position of needing to be a reaction to the Mourinho reign.
He would take any kind of win on Sunday but increasingly supporters want a display on which to hang their hats, to illustrate that Nuno is up to the job of meeting the best traditions of the club. There were few genuine conclusions to draw from the thrashing of Mura, who are the lowest-ranked side playing European football this season, according to UEFA’s coefficient model.
Nuno’s decision to introduce Kane, Heung-min Son and Lucas Moura on the hour, shortly after Mura had halved the deficit through a wonderful Ziga Kous volley, turned the game definitively in Tottenham’s favour but whiffed slightly of desperation and reflected the pressure on the manager, whose fringe players have already squandered a 2-0 lead once this season.
Spurs really should not need Kane, Son and Moura to guarantee a win in this type of match, and their introductions spoke to the pressure on Nuno.
That said, a comfortable rout in the final 30 minutes was a much-needed confidence boost and offered further evidence that Kane has no problem finding the back of the net, provided he is in the right positions.
The England captain’s goals were all clinical, close-range finishes, and part of Nuno’s tactical challenge against Villa will be to ensure his talisman has better service in goalscoring positions.
Even considering the quality of the opposition, there were also green shoots in terms of style against the Slovenians, with Nuno switching to a 4-2-3-1 system which has always felt the best fit for Spurs.
Dele Alli had another inconsistent game but looked far happier back at No10, winning and scoring an early penalty after a trademark burst into the box. If Dele is to resurrect his career, it will have to come with consistently decisive displays against far better opponents, but playing to his strengths is a good start.
Giovani Lo Celso doubled Spurs lead inside eight minutes and also caught the eye, while Cristian Romero and Joe Rodon looked Spurs’s most comfortable centre-half pairing with the ball at their feet. There are some building blocks for Nuno, then, ahead of the Villa game.