It was the second minute of stoppage time when the ball left Roberto Firmino’s foot, when Jürgen Klopp set off on his victory run amid a crescendo of noise inside Anfield. And in that moment, even though these are only the early stages of the Champions League, perhaps we learned some more about last season’s beaten finalists.

We knew they played their home games with fearlessness. We knew they attacked in numbers, that they went for the jugular and that nobody, but nobody, would persuade them to change that policy. But now we can safely say the modern Liverpool have powers of endurance to go with all their other gifts.

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Another team might have lost their way after that moment in the 83rd minute when Kylian Mbappé decided it was time to introduce himself to Anfield properly – inside the penalty area, with the ball on his right foot, and burying his shot so confidently it felt necessary to remind yourself this player, holding the keys to the football universe, is a boy of 19.

Briefly, Liverpool even toyed with the idea of losing a game they had once led 2-0. Only briefly, however. Klopp’s men quickly shook their heads clear, rousing themselves for one final onslaught and conjuring up the winner after harrying Mbappé into a mistake in his own half. Firmino, a 72nd-minute substitute, had started on the bench because of the eye injury he suffered against Tottenham on Saturday. He celebrated his winner by cupping the affected eye – yet there was nothing wrong with his vision when he beat Alphonse Areola with a low diagonal shot from right to left.

That goal, and the match as a whole, should be added to the growing file of evidence that Anfield, without any exaggeration, may have legitimate claims to be thought of as the most difficult place for any team to visit in the Champions League right now.

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Another team might have chosen to play with restraint given the opposition included Mbappé on the right, Neymar on the left, Edinson Cavani through the middle and Angel Di María never too far away. Not Liverpool, though.

The team in red played as if affronted by the suggestion that the opposition had the better selection of attacking riches. Liverpool did not reach the final last season with conservatism and, once again, they could be seen trying to rush the opposition players off their feet, swarming forward and, in the first half, rekindling the thought it is amazing how many times European opponents concede a goal in front of the Kop, become unnerved and quickly let in another one.

Perhaps an argument could be made that Liverpool should have closed down the game after establishing a two-goal lead, 36 minutes in, courtesy of Daniel Sturridge’s header and a penalty from James Milner.

Facebook Twitter Pinterest Daniel Sturridge rises to power Liverpool into an early lead. Photograph: Tom Jenkins/Guardian

Sturridge was making his first Champions League start and opened the scoring, on the half hour, by heading in Andy Robertson’s cross. At 2-1 he missed what was probably an easier chance, failing to get any power with a header. Overall, however, he can reflect on a satisfying evening’s work, no matter that Firmino was still, ultimately, the hero.

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PSG were certainly rattled during the period in the first half when, six minutes after going behind, Juan Bernat’s challenge on Georginio Wijnaldum gave away the penalty. It was not a wild challenge, just a risky and slightly unnecessary one. Milner, one of several outstanding performers for Liverpool, slotted the penalty past Areola, aiming to the goalkeeper’s left.

Even at that stage, however, with Wijnaldum and Jordan Henderson also excelling, there was always a lurking danger. Neymar, for starters. The Brazilian began the game with a body swerve to glide away from Trent Alexander-Arnold and then a slaloming run past, in order, Henderson, Sadio Mané and Milner.

The crowd enjoyed it later in the first half when Neymar was flattened by Milner’s hard but fair challenge and, again, when Mané went past the Brazilian with some showboating of his own. But it was also clear PSG had the personnel to believe a feat of escapology was possible.

Their comeback began five minutes before half-time. Di María supplied the cross from the left and Cavani’s attempt at an overhead kick connected with only thin air. The ball bounced off Robertson and Thomas Meunier, venturing forward from his right-back position, hooked a splendid left-foot volley past Alisson.

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Until the equaliser, there were only fleeting glimpses of Mbappé’s menace and only one occasion early in the second half that he managed to get past the quick, alert Robertson. Di María’s link-up play with Neymar was a prominent feature. As a front three, however, Neymar, Cavani and Mbappé still looked a work in progress.

Liverpool were determined not to sit on their lead and there were prolonged celebrations after Mohamed Salah stabbed in a loose ball, believing he had made it 3-1, only for the Turkish referee, Cuneyt Cakir, to signal that he had not missed Sturridge’s studs going into Areola’s midriff after all.

It was the correct decision and Sturridge’s missed chance to make it 3-1 looked like being a costly lapse when Salah gave away the ball in the buildup to Mbappé’s goal, with Neymar’s initial run opening up the chance for the French World Cup winner.

Yet Liverpool still found a way to win, even with Salah being substituted, and created an unhappy sense of deja vu for Thomas Tuchel, the PSG manager who also lost in stoppage time when he came here with Borussia Dortmund in the Europa League quarter-finals in 2016.

• This article was amended on 19 September 2018 because an earlier version misspelled Alisson’s name as Allison.