Finally, at 11.52pm local time, the last kick of an epic night. Eric Dier, England’s fifth penalty-taker was setting off on his victory run, soon to be submerged by his teammates. Gareth Southgate had forgotten, yet again, he was supposed to be nursing a dislocated shoulder and here was the hard proof that England, contrary to the impression they might have given for much of the previous 30 years, did know how to win a penalty shootout, after all.

It was a euphoric and nerve-shredding finale and these are the moments, surely, when England’s followers could be forgiven for daring to dream that something special is building, something exhilarating and rare. Yes, it would be dangerous to get too carried away but right here, right now, to hell with anyone who insists it is time for restraint. England have arrived in the quarter-finals and the World Cup is suddenly filled with all sorts of new possibilities.

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This was their first knockout victory in a World Cup for 12 years. It was only their seventh, in any major tournament, since 1966, and now they face Sweden on Saturday for the right to play Russia or Croatia in the semi-finals.

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Southgate had told us he wanted England’s penalty-takers to “own the process” and they did just that, eventually. It was a close-run thing but Jordan Henderson’s miss – or, rather, David Ospina’s save – mattered little in the end because of Mateus Uribe hitting the crossbar with Colombia’s fourth effort and Jordan Pickford saving the next one from Carlos Bacca, ensuring Moscow 2018, will be remembered much more happily than Turin 1990, Saint-Etienne 1998, and Gelsenkirchen 2006, and not forgetting the European Championships at Wembley 1996; Lisbon 2004 and Kiev 2012.

An hour after the match, England’s supporters were still partying at one end of the stadium. They did not want to leave and who could blame them when, after three penalties each, England were one down and staring at another harrowing story of deja vu?

Dier joined Harry Kane, Marcus Rashford and Kieran Trippier in showing why all that practising of penalties on the training ground was necessary. Kane had also scored from 12 yards to give England the lead shortly before the hour and it was not until the third minute of stoppage time that Colombia prolonged the match by concocting the equalising goal. Another team might have wilted after such an agonisingly late equaliser. That, however, was one of the more impressive parts of England’s performance. Dier might have won the match with a free header in the second period of extra time. Danny Rose, another of England’s substitutes, had a golden chance and in the extra 30 minutes there was hardly a single moment when it felt as though Southgate’s players might go under.

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This was only England’s second shootout victory in eight attempts at major tournaments, the other coming against Spain in Euro 96, and in the process they answered so many questions about their nerve and temperament for the big occasion. Ever since he took the job Southgate has been asked whether his team could cope when the heat of the battle was dangerously close to intolerable. We know now that, yes, they do. Yet the shootout was only part of the story against tough, obdurate opponents – “animals” according to Chris Waddle in his radio commentary – on a night when Colombia’s supporters had filled this stadium in swathes of bright yellow, bouncing and swaying like human blancmange and creating a raucous din.

They bellowed the words of their national anthem – Oh gloria inmarcesible – and outnumbered their English counterparts in a way that is rarely seen. Yet just consider, for example, Kane’s competitive courage when he had his first penalty and Colombia’s players, to put it bluntly, lost the plot about the decision to penalise Carlos Sánchez for grappling him to the floor at a corner. The protests were so chaotic Kane’s penalty was delayed by almost four minutes. What nerve the captain showed to improve his position at the top of the Golden Boot scoring chart – his sixth goal and his third penalty.

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Colombia might have been missing the injured James Rodríguez but they still occupied a superior rung of the football ladder to Tunisia or Panama or the scratch Belgium XI who England encountered in the group stages. But Southgate’s team were never cowed. The manager had instructed them to play with freedom, to show adventure, to hold out their chests and demonstrate they knew how to take care of a football, too. True, they found it difficult to get behind the Colombia defence and looked more dangerous from set pieces rather than open play. Yet their opponents barely troubled Pickford throughout 90 minutes and that in itself felt like an achievement against a side featuring Radamel Falcao, Juan Cuadrado and Juan Quintero.

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The evening might have been a lot more straightforward if the correct decision was made, towards the end of the first half, when Wilmar Barrios took exception to Jordan Henderson’s proximity to the defensive wall and dealt out his retribution by lifting his head into his opponent’s jaw. Henderson ended on the floor and Barrios was so lucky to escape with only a yellow card he could be seen shaking the hands of the match officials at half-time.

The uproar before Kane’s penalty was shocking in other ways but Southgate had told his players not to react to the provocation and, in that respect, the game against Panama was a valuable lesson.

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Colombia still had more than half an hour in normal play, plus five minutes of added time, to concoct an equaliser. They spent most of that time arguing with the referee, feigning injuries and trying to pick fights. But then, in the 93rd minute the substitute Uribe let fly with a 30-yard volley. Pickford’s flying save was exceptional but it was Yerry Mina against Harry Maguire at the resultant corner: Colombia’s tallest player against England’s. The man in yellow won the header, the ball bounced off the turf and Trippier did not have the height to stop it on the line.

Would it be the same old story for England? It felt that way after Falcao, Cuadrado and Luis Muriel scored Colombia’s first three penalties of the shootout. Instead, Pickford had a heroic role in the victory. Dier’s penalty was not entirely convincing but Ospina was face down, distraught, and the victory run was under way.