Seriously, where do you even start? It was a wild and eccentric night, full of drama and incident, and when the players of Tottenham finally manage to catch their breath they can start looking forward to a Champions League semi-final.

They had blown a gaping hole in Manchester City’s hopes of an unprecedented quadruple and, in the process, reached the last four of this competition for the first time. Their celebrations at the end were long and joyous.

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That, however, tells only part of the story from a match when City led 1-0, trailed 2-1 and then went ahead 3-2, all in the opening 21 minutes, even before we get to the throbbing drama of a second half in which both teams scored again – decisively, as it turned out, for the Spurs substitute Fernando Llorente – and Pep Guardiola’s team had to endure the stoppage-time ordeal of believing Raheem Sterling had conjured a late, dramatic winner.

It would have been Sterling’s hat-trick and, coming in the 94th minute, almost certainly the killer blow. And in those moments, with some of the early-leavers rushing back into the stadium to join in the raucous celebrations, it felt like City had pulled off a remarkable feat of escapology. Except football has changed. No offside flag had gone up but VAR had the benefit of action replays and it showed Sergio Agüero had strayed marginally past the defensive line when the ball came to him in the buildup.

Facebook Twitter Pinterest Fernando Llorente scores to make it 4-3 on the night. The goal was checked by the VAR for handball, but was awarded. Photograph: Mark Cosgrove/News Images/Rex/Shutterstock

As if that were not galling enough for City, VAR had gone against them in the 73rd minute when Llorente bundled in a corner for what was ultimately the decisive goal. Should it have stood? The Turkish referee, Cuneyt Cakir, took an age to make up his mind and, even then, he did not seem sure. His first reaction was to hold out his arms as if to say he was uncertain. In the end, he signalled the ball had struck Llorente on a thigh. And that meant Spurs were ahead again, on the away-goals rule.

City’s players had argued the decisive contact came off Llorente’s elbow but maybe, in time, they will come to reflect it was not VAR to blame for their elimination but their inability to score an away goal.

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Spurs managed two inside the opening 10 minutes and both times Son Heung-min put the ball past Ederson the calculations changed again. The first one meant City needed at least three to go through. Three minutes later, Son had his second goal and that meant City required four. Yet they already had one courtesy of Sterling’s first, four minutes in, and when Bernardo Silva made it 2-2 the complexion of the game changed again.

Spurs had been ahead barely a minute. Then Sterling popped up again to put in the next one and, for long spells, Spurs had to withstand an onslaught.

It was certainly an absorbing spectacle, containing all sorts of possibilities, as the game swung in favour of the home side, then the away team, then back again, even before we had reached half-time.

Quick guide Champions League semi-final fixtures Show Hide Tuesday 30 April: Tottenham v Ajax Wednesday 1 May: Barcelona v Liverpool Tuesday 7 May: Liverpool v Barcelona Wednesday 8 May: Ajax v Tottenham Champions League final to be played in Madrid on Saturday 1 June

It was rare to see a Champions League quarter-final being played so openly and, though it did not matter a great deal ultimately, Spurs really ought to have made it a more straightforward match once Son’s goals had opened up a 3-1 aggregate lead. Instead, City’s next goal arrived so quickly it meant there was never a concerted period during that bewitching, often bewildering, first-half blitz when Guardiola’s players looked out of it. Bernardo Silva’s shot deflected in off Danny Rose for the equaliser and, yet again, it was game on.

For Spurs, the frustration during that breathless opening period was that both of City’s goals had come from dangerous opponents eluding their markers. It was the same again when Sterling stole in from the left to turn in Kevin De Bruyne’s right-sided delivery for the goal that made it 3-2. De Bruyne had also set up Sterling to cut inside and pick out the far corner with a curling right-foot finish for the first goal. Sterling’s next one was from closer range, this time with his left foot, his 22nd and 23rd of the season.

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Spurs certainly rode their luck at times and, yes, a more experienced team might have changed the pace of the game after the initial rush of goals. Mauricio Pochettino’s side would have been castigated if they had thrown it away. Yet they were always dangerous and seemed to realise that City, minus Fernandinho at the start, might be vulnerable through the middle. They were rewarded for their adventure and Son gave the impression he may have been affronted by the suggestion they would miss the injured Harry Kane.

His second goal, in particular, was a beauty, an elegant shot into the top corner after a move that started with Aymeric Laporte losing the ball inside his own half. Laporte had also been culpable for Son’s first goal when the defender accidentally turned the ball into the path of the scorer. Son, playing with immense confidence, let fly with his right boot and the ball skimmed beneath Ederson, who should probably have done better.

That the score remained 3-2 throughout the remainder of the first half felt like a goal drought. Yet City still had an entire 45 minutes to go for more and when Agüero lashed in their fourth goal they were ahead on aggregate for the first time.

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Again the brilliant De Bruyne was involved. Agüero was close to the position where he scored what they know here as the 93.20 goal. This time, however, it was not decisive. The truth is Llorente’s goal went in off both an elbow and a thigh. Spurs had VAR on their side but they had also played with great togetherness and ambition. Now they can start preparing for a semi-final against Ajax.