High in the Olympic stadium, the flares were lit. Way below, Kylian Mbappé had lept over the advertising boards and was running towards the 3,000 supporters who had travelled from France, his teammates chasing him across the track, celebrating wildly. There was a solitary minute remaining and, for all their domination, it had been on edge, but now it really was over: Paris Saint-Germain are heading into the semi-final of the Champions League, overturning a 3-2 first leg defeat at the Parc des Princes with a 4-1 victory in Catalonia; Barcelona, for a sixth season in a row, are not.

This time, though, there was no collapse, and no shame. Barcelona had won away and although they had suffered here, they had competed against a side who may well be considered a favourite to reach the final, hanging on long enough to launch a late reaction that allowed them to believe in a way back, one last, unlikely chance. In the final minute, though, that hope was taken away when PSG, who had come from one down from the first leg and one in the second to lead 3-1 here, were able to run.

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Achraf Hakimi led the charge, dashing up the Montjuïc home straight to set up Mbappé. Marc-André ter Stegen saved the first shot, then stopped the second from Marco Asensio, but the ball fell to Mbappé again, who scored his second. “The players kept the faith,” Luis Enrique said, and now the happiness they felt was “bestial.” It had been hard, the PSG coach said to face his former club, and not something he wants to do again soon.

It had been hard for Barcelona too, players in tears at the end. A goal up through Raphinha, they had seen a red card for Ronald Araújo after half an hour and been forced to resist PSG for just too long. The card, Xavi insisted, changed everything, responding with a sharp “no” when asked if he agreed with Luis Enrique’s claim an impressive PSG side would have won anyway. “I told the referee he was a disaster,” Xavi admitted. “Eleven against 10 is almost impossible; the decision destroyed the game.”

Which is not to say nothing happened thereafter; plenty did. At the heart of so much of it was Ousmane Dembélé, the former Barcelona player whose every touch was whistled here. He, Bradley Barcola and Mbappé gave PSG a 3-1 lead that they might have extended earlier but which they ended up having to hold onto.

Luis Enrique insisted that PSG’s opening was “marvellous”. Pau Cubarsí had to slide in on Mbappé, Araújo did the same to Dembélé, and Frenkie de Jong had to block a shot from Vitinha, all inside the opening three minutes. A second blocked shot followed soon after and, at this early stage, Barcelona could not find a way out. The first time they did, though, they scored, the goal wonderfully made by Lamine Yamal, who is only 16 for goodness sake. Dashing past Nuno Mendes, he very nearly made it all the way to the near post, where he pulled back. With Gianluigi Donnarumma out of position, Raphinha ran in to finish.

Alas, Yamal was not around much longer and nor was Araújo, both gone within 12 minutes. Barcola was released and Araújo went after him, a heavy hand on the shoulder enough to see the PSG winger go down, the referee Istvan Kovacs sending him off, despite Araújo’s claim that Cubarsí was there to cover and that it was shoulder-to-shoulder. Yamal was the man – the boy – sacrificed.

Ter Stegen had already made a superb save from Mbappé, Jules Koundé then clearing off the line, and now PSG smelled blood. Barcola and Dembélé in particular caused problems and combined to get the goal that levelled this, the former sending a pass across the six-yard box for the latter.

Barcelona still had a two-goal lead but it was increasingly precarious. Vitinha shot over, Barcola volleyed wide and Mendes dropped a cross just behind João Cancelo which Dembélé volleyed fractionally past the post. It was PSG’s 11th effort – Barcelona had two – and they soon added to it. Ter Stegen palmed Hakimi’s shot and Mbappé then set up Fabián Ruiz, who dragged wide before Vitinha’s low shot from twenty yards levelled the tie.

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Immediately, Ilkay Gündogan clipped the post but Dembélé inflicted further damage, taken out by Cancelo for the penalty from which Mbappé scored the third. Barcelona looked broken and there was something desperate in Gündogan’s attempt to win a penalty but while the difference between the teams felt huge now the margins remained fine and as long as there was only one goal in this, it wasn’t done.

Supplied by Raphinha, Robert Lewandowski almost levelled it but Donnarumma made a sharp save, Marquinhos just beating Ferran Torres to the loose ball. Raphinha then escaped Lucas Hernández and shot wide. The noise rose, so did the PSG nerves, Lewandowski denied by Marquinhos with two minutes left. Raphinha almost curled the corner straight into the net, Donnarumma pushing over for another. This was it. One last chance, or so they thought. Suddenly though, PSG were dashing clear, Hakimi dashing the length of the Olympic stadium to the other to end it.