This match had an epic ­quality throughout and was decided by a moment that will enter ­Turkey’s football folklore.

They were ­clinging on to their lead amid rain, smoke, ­excruciating whistles and a ­barrage of Austrian pressure when ­Alexander Prass looped a long, deep cross towards the far post in hope rather than expectation. It arced to ­Christoph Baumgartner, who had pulled away from his man and hung high in the Leipzig sky, and the next thrilling act seemed set. There was little wrong with the header, directed downwards and skipping sharply up. How Mert Gunok, the Turkey goalkeeper, reacted to paw the ball up and wide is a thing of wonder and, after one last corner was seen off, the celebrations could start.

Related: Austria 1-2 Turkey: Euro 2024, last 16 – live

Gunok joined his teammates partying in front of the Turkey support, decibel levels surely ­exceeding anything heard in Germany all summer. At the other end a ­tearful ­Baumgartner, who could have scored a hatful, had to be consoled by a member of Austria’s staff.

Unbridled triumph on one side and, opposite, a sense of sporting tragedy. A dose of revenge, too: much as Vincenzo Montella had attempted to play it down beforehand, he and his players had been desperate to ­settle a score after the 6-1 thrashing they received in Vienna just over three months back.

More importantly than any tit-for-tat, Turkey are in the quarter-finals. Their wild, highly strung roadshow will career to Berlin for more appointment ­viewing against the Netherlands and ultimately they deserved to go through. Montella’s players were out on their feet in those dying moments, their opponents’ appetite to run, run and run some more finally threatening to wear them down.

But they were tough, technical and composed when it mattered for the majority. The occasion had been billed as a clash of Turkey’s emotion and Austria’s mechanised drills, yet the end product should be framed as a triumph for Montella. He packed the centre of the pitch and, in the first half at least, it meant Austria could not quite execute their usual swamping job. Even in the absence of their captain and heartbeat, Hakan Calhanoglu, they were able to execute their game plan and bite hardest when it mattered.

In the afterglow of a match this gloriously pulsating, though, discussion of tactics may be for the birds. It was ­bedlam from the beginning, six Austria ­players hurtling into the opposition half from kick‑off and Gunok having to smother at Marcel ­Sabitzer’s feet almost immediately. Their propensity to score early goals is well documented so the only surprise was that, when one came, it was Turkey who profited. Proceedings were still well inside the opening minute when ­Turkey won a corner, the defender Kaan Ayhan whirling his arms to work the crowd into a higher state of frenzy in case that were possible.

Arda Guler swung the ball in from the right side and the delivery completely flummoxed Austria’s defence, almost creeping straight in before Baumgartner blocked on the line. He could only clear against Stefan Posch at point-blank range and the ball was goalbound once again until Patrick Pentz scooped clear. That reprieve lasted a millisecond: Merih Demiral smashed the loose ball in and Turkey were ahead after 57 seconds.

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The promised level of chaos had already been hit. Baumgartner shot just wide straight afterwards and saw Demiral somehow divert a corner from in front of him on the line: he had hoped for a triumphant outing at the stadium he calls home, but he and the rest of Austria’s Red Bull school were ultimately consigned to look on as Turkey turned it into theirs.

Further half-chances arrived for Baumgartner and Philipp Lienhart but Turkey looked increasingly comfortable as the interval neared. Confident, too: the outstanding Guler offered a flourish in attempting to beat Pentz from halfway, the ball sailing wide. Demiral, a centre-back who approached his tasks in each box gladiatorially, missed a good headed opportunity but atoned soon enough.

Austria had ripped into the second period, Ralf Rangnick rolling the dice with two changes and seeing Gunok block from Marko Arnautovic after they had finally shown some subtlety in the middle. The giant substitute Michael Gregoritsch headed wide and Konrad Laimer shot waywardly before the sting arrived from the same one-two as before.

Guler was pelted with plastic cups as he shaped to take another corner but was undeterred from whipping in another gorgeous delivery that Demirel converted emphatically after rising above Kevin Danso.

Game over? Not here. It never quite seemed likely and Gregoritsch, jabbing in after Stefan Posch had headed on yet another set piece, set up an exhilarating finale. Turkey squandered chances on the break but the luckless Baumgartner, beating Gunok to the ball on one occasion, missed two headers and Austria’s siege could not break through.

Then Gunok had his biggest moment of all. Rangnick was asked whether the save reminded him of Gordon Banks. “That is correct,” he said, leaving any other sentiments to float in the air. For Turkey and their relentless contingent, the atmosphere is now thick with awe and promise.