“Ad augusta per angusta” – through difficulty to honour – the banner that stretched across the south stand of the Metropolitano had said, and it was right. Oh, how, it was right; more even than they had imagined. They would struggle and they would suffer, a wild night lived on the edge, one in which even the manager got injured, but in the end there was glory for Atlético Madrid.

A game that could have gone any way, won or lost several times over, eventually went to the spot. And there, at 23.43pm local time, Lautaro Martínez of all people sent the ninth penalty high into the north end.

For the first time in 2024 Internazionale did not win a football match and it cost them in the cruellest way. It was nearly a decade since there had been a shootout in this competition; now there have been two in as many days. There had been 38 shots here, Atlético winning the game 2-1, but they would need nine more to decide this battle.

Last year’s finalists are out; Atlético are through, the substitute Memphis Depay dragging them into extra time with a late goal and an almost superhuman display, then absolutely belting his spot-kick into the net before Jan Oblak took flight to save twice and sent them through.

A first-leg defeat had been overturned. So had a first goal conceded in the second. Atlético had overcome Saúl Ñíguez missing their second penalty, too. He was denied by Yann Sommer but Alexis Sánchez and Davy Klaassen were denied by Oblak. Atlético had done it, elation eclipsing the exhaustion here. They had been running flat out for two hours; all of them had. Even the ball boys had been dashing about from the very beginning, as if those opening minutes were actually the final ones. Nothing though could be as intense, as heart-stopping, as the final stages became.

Seeking a way back after San Siro, it took just three minutes for Atlético to fire an effort on target, through Stefan Savic – already more than they had managed in the whole of the first leg – and they might have had an early lead when Samuel Lino bounced off Nicolò Barella, got away from Stefan de Vrij and hit a hard low shot that Sommer to saved.

And yet to begin with there was a clarity and incision about Inter that suggested this game might actually be settled early, an example of their ability coming when Denzel Dumfries forced Oblak into a double save, and the goal coming on just 33 minutes.

When Federico Dimarco finished a slick move built by Martínez, Henrikh Mkhitaryan, Alessandro Bastoni and finally Barella, you could be forgiven for thinking this was done. High in the away end, Italians lit up their phones but were still being waved when Atlético equalised, a slightly comic goal changing the feeling here. And, ultimately, the outcome. Benjamin Pavard made a mess of a clearance, swiping, missing and falling, to leave Antoine Griezmann alone to score.

The Frenchman should have added to that when he was set up by Marcos Llorente early in the second half, but shot at Sommer. When ­Llorente again escaped a moment later, Álvaro Morata scuffed over when he would have been better letting the ball go. At the other end, Inter should have ended it, Martínez slipping in first Marcus Thuram and then Barella only for them to waste golden opportunities, setting up a frantic, open finale in which Atlético threw everything at Inter.

Memphis especially: sent on, what an impact he had, with three chances in not many more minutes. Spinning a couple of yards from goal, he could not quite finish when Ángel Correa created the first. Then on 85 minutes, he thudded a shot off the inside of the post. And then with three minutes left he turned sharply in the area and struck a superb finish, this place exploding.

Diego Simeone pulled up injured as he raced to join his celebrating ­players, then ended face down on the turf when Griezmann set up Rodrigo Riquelme to win it with 20 seconds left. This was it, the moment, but the shot flew over. That had hurt, but Riquleme would redeem himself from the spot.

Like the footballers, Simeone got up again, even as muscles and lungs screamed. Extra time began with Yann Bisseck’s cross giving Thuram a headed opportunity, then Riquelme delivered for Memphis, whose shot was somehow saved by Sommer, and back at the other end, Martínez nodded fractionally wide.

The nerves were frayed, the clearances hacked, desperation everywhere, heroism and generosity of spirit too. The ­players were in pieces but ran all the way to the end, which is when they were put on the spot, more difficulty and ­honour awaiting them.