The drama was unremitting but when Ivan Rakitic strode forward to address the penalty to win it for Croatia, he located a pocket of calm. The Barcelona midfielder had been in the same position last Sunday, standing over the shootout kick to beat Denmark in the last 16, and he had risen to the challenge.

He would do likewise here and, in truth, it never looked in doubt. When Rakitic picked out the bottom corner, Croatia’s joy knew no bounds. At last, they have emulated the glory boys from France 98, who reached the semi-finals, and it is they who have advanced to face England in the last four.

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Croatia thought they had won this quarter-final before they actually did. Domagoj Vida will not rate his extra-time header as the most powerful of his career but it was surely the most precious.

When he connected with Luka Modric’s corner, the ball had a long way to travel. It got there in the end. The substitute Vedran Corluka had a nibble at it and another replacement, Russia’s Fedor Smolov, was on the scene. The upshot was that the goalkeeper, Igor Akinfeev, saw it late and it squeezed into the far corner.

It was merely the precursor to an extraordinary finale.

At this point, it is probably worth remembering what a mess Russia were in before the start of their World Cup. Winless in seven matches, they were derided as the worst team in the nation’s history. They were the lowest-ranked side here. Nobody gave them a prayer.

But the remarkable last-16 shootout win against Spain, which followed a largely positive group‑phase campaign, had ignited belief in a seemingly impossible dream. Russia were determined to meet England in the semi-final and, even when extra time was finished, they refused to give up.

Mário Fernandes’s equaliser sparked wild scenes, with all of Russia’s substitutes tearing on to the pitch and hurdling the advertising hoardings behind the goal to celebrate with him. The right-back had headed home from Alan Dzagoev’s free-kick and the momentum, at that stage, was most assuredly with his team.

On into the shootout and Russia began badly when Smolov’s attempted panenka was weak and Danijel Subasic saved. When the Croatia substitute Mateo Kovacic was denied by Akinfeev in round two, it was all square but there would be a horrible twist to Fernandes’s evening when he dragged the first kick of round three past the post.

Facebook Twitter Pinterest Ivan Rakitic celebrates after scoring the winning penalty. Photograph: Shaun Botterill/Getty Images

Croatia knew it was going to be their night when Akinfeev pushed Modric’s kick on to the inside of the post and watched it flash across the line and go in off the far post. Rakitic would see them home.

With several of their stars including Rakitic, Modric, Subasic and Mario Mandzukic the wrong side of 30, it feels as though it could be now or never for this Croatia team in terms of football’s biggest prize. They continue to believe it will be now.

It was difficult not to feel sorry for Stanislav Cherchesov and his Russia players. They gave everything, playing with no little adventure, which had been a surprise after their bolted‑door approach against Spain, and they rattled Croatia in the first half. Denis Cheryshev, one of the finds of the tournament, had scored his fourth goal of it – and what a goal it was – yet the tie turned against them when Andrej Kramaric equalised just before half-time. It was a bad time to concede.

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In the end, the shootout gods were against them but there can be no doubt that the performances of this team have energised the nation and the World Cup. Russia supporters will take away cherished memories. It was their first quarter‑final since 1970, when they competed as the Soviet Union, but there would not be a first semi‑final since 1966.

England’s scouts will pore over every detail of the Croatia performance, not least how Zlatko Dalic left out the defensive midfielder Marcelo Brozovic at the outset to play an extra attacking player in Kramaric. Dalic’s starting central midfielders were Modric and Rakitic. But he would introduce Brozovic in the second half of normal time and press Modric and Rakitic further forward either side of him in a 4-3-3 formation. Croatia came to control the midfield in the second half and Modric was particularly prominent.

Play Video 0:45 Croatia fans celebrate World Cup quarter-final win as Russians are left devastated – video

Russia pressed high in the first half with Aleksandr Golovin, the No 10, playing like a second striker and Artem Dzyuba, the centre-forward, a focal point and battering ram. It was impressive to see the home nation’s slickness and directness.

Cheryshev scored after he swapped passes with Dzyuba and, from a position to the left of centre – 25 yards out – he bent a curler that began its journey outside Subasic’s right-hand post before fizzing back inside it. Subasic did not even dive. It was a beauty and the home crowd could revel in another pinch-me moment.

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Croatia might have been in front by then. Ante Rebic, the powerful winger, sent a free header high following a corner and Mandzukic fluffed a finish from Sime Vrsaljko’s cross. They found the equaliser when Mandzukic crossed and, with the Russia defence pulled out of shape, Kramaric arrived to head home. Briefly, there was the sound of silence.

Ivan Perisic hit the inside of the post for Croatia on the hour but Russia continued to flicker, with the substitute Aleksandr Erokhin heading over. It was a gripping spectacle, the atmosphere pulsating, but it would be Croatia who felt the pull of destiny.