So, where does this register in the list of spectacular European nights for Manchester United? Very high, presumably, judging by the scenes of euphoria after Marcus Rashford’s decisive penalty, deep into stoppage time, and the victory run at the final whistle when every single player, pursued by a small army of backroom staff, was haring towards the away supporters to celebrate.

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If Ole Gunnar Solskjær has not already secured himself the job on a full-time basis, surely the announcement must be soon. He had told us there was no such thing, in the world of this extraordinary football club, to believe a two-goal deficit could ever be a lost cause. He had spoken about the importance of scoring first and how, in happier times, United had a remarkable knack for encountering glory with moments of late, nerve-shredding drama. And more fool anyone who did not believe him.

As it turned out, Solskjær’s confidence was not misplaced judging by the story of how his team made it through to the quarter-finals, featuring an almost improbable comeback and a clear statement of intent from this once-mighty club, after everything they have endured since Sir Alex Ferguson’s retirement, that they still want – and deserve – to be taken seriously at elite level.

Ultimately, it is only a small detail that, over the two legs, PSG had looked the more competent side for long spells. No team in the history of the European Cup has gone through after losing 2-0 at home in the first leg and United, lest it be forgotten, managed it after arriving in the French capital without 10 players. Mason Greenwood, making his debut, and Tahith Chong, another academy product, were both on the pitch when Rashford struck the decisive penalty. It was an extraordinary finale and, amid all the jubilation and chaotic celebrations, there was one cry from the away end that rang out loud and clear. “United are back,” it went, over and again.

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In that sense, it was an old-fashioned, almost nostalgic, kind of victory, going back to the times when Ferguson liked to boast no other football team on the planet scored so many late winners. In another sense, it was a very modern occasion, culminating in the Slovenian referee, Damir Skomina, being alerted to a possible handball from Presnel Kimpembe inside the penalty area. The video replays went in United’s favour and Rashford held his nerve brilliantly when faced with the challenge of trying to get the ball past Gianluigi Buffon from 12 yards.

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For PSG, there was desolation. The champions of Ligue 1 will be accused of cowardice, of bottling it, and all the usual insults. That would not be quite fair, however, on a night when they had 87% of possession at one point. PSG easily had enough chances to spare themselves what happened in the 94th minute. They hit the post, they pinged shots at David de Gea and they had a goal disallowed, as well as a penalty appeal of their own.

It made for incredible drama amid the kind of din that made it easy to understand why Parc des Princes is described locally as the caisse de résonance. United never succeeded in silencing the “box of sound”. They did, however, produce an unprecedented European Cup story with a cobbled-together midfield of Fred, Scott McTominay, Andreas Pereira and Ashley Young. Eric Bailly was injured in the first half and, as well as Chong and Greenwood, the away side had Angel Gomes and James Garner on bench. When was the last time, if ever, United went into such a key night with the shirt numbers of their substitutes totalling 240?

David de Gea consoles Kylian Mbappé after the full-time whistle.Photograph: Geoffroy van der Hasselt/AFP/Getty Images

Solskjaer, however, had made the point that the complexion of the night could change dramatically if his team scored first. Romelu Lukaku’s first goal was timed at one minute and 51 seconds. His second came just before the half-hour mark and on both occasions it was preceded by an error from one of PSG’s players. Thilo Kehrer’s misplaced pass led to the first one. Buffon, of all people, made the mistake for the next one, spilling Rashford’s swirling long-range shot, and those were moments to encourage United belief that PSG might be vulnerable, after all.

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For a while, however, it did seem as though Solskjær might have been mistaken. At 1-0, the response from Thomas Tuchel’s players was swift and impressive. They were level in the 11th minute and, after that, the paradox of the first half is that there were parts of it when United found it immensely difficult to cope with the speed and movement of Kylian Mbappé, Ángel Di María and Dani Alves. Incredibly, it was not until the 22nd minute that Young had his first touch of the ball – and that was a tackle. Juan Bernat, PSG’s attacking left-back, scored the equaliser from Mbappé’s pass across the six-yard area and, at that stage, it seemed as though Solskjær’s players might capitulate.

Except, of course, they had hard evidence of their own that they could hurt PSG, too. Lukaku’s first goal was a classic piece of centre-forward play, latching on to Kehrer’s mistake, holding off Kimpembe, then taking the ball wide of Buffon and sliding in his finish from a difficult angle. The second goal was also about anticipation. Buffon’s goalkeeping was poor, attempting to hold a shot from Rashford that moved dramatically in the air, and Lukaku was ready, pouncing on the loose ball to score again from close range.

If nothing else, that meant the game could not go to extra time. One team had to win in normal time and the night was still full of possibilities for both sides. The game was brilliantly poised and for United it was a backs-to-the-wall operation at times. Then, finally, the referee was making that now-familiar rectangular sign. “VAR,” the away end chanted, with no real idea of what had happened. Rashford was sizing up Buffon and United, as the song went, really are back. Football, bloody hell – the Solskjær version.