Arnor Ingvi Traustason supplied the rip-roaring dream climax to this match when, with the very final touch of the ball, he finished past Robert Almer to claim a scarcely believable winner and continue Iceland’s fairytale at this European Championship.

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Traustason slid as he connected and for a moment appeared unsure if he had actually scored or hit the side-netting. When the 23-year-old looked again and realised he had registered, up he rose to his feet and what followed was bedlam, as high emotion gripped the Stade de France.

Just about all of Iceland’s staff rushed on to the field to mob Traustason and amid these unforgettable scenes and sky-splitting noise the referee Szymon Marciniak blew for full time. It meant Heimir Hallgrimsson and Lars Lagerback’s men had finished second in Group F and will play England in Nice in the last 16 on Monday.

Traustason was the hero of the hour and his story has a touch of fantasy as he did not feature in any of Iceland’s qualifiers for this tournament – making his debut last autumn – and the midfielder had entered here only 10 minutes from time.

Iceland lined up in their familiar 4-4-2 and Austria were arranged in a shape-shifting formation that was a nominal 3-4-2-1, with Christian Fuchs and Florian Klein the wide men in midfield and an attacking trio headed by David Alaba. This approach from Marcel Koller caused surprise among their opponents as the coach had not fielded a back three previously at Euro 2016.

The pitch-side air was muggy but this did not stop Charlton Athletic’s Johan Gudmundsson enjoying a flying start, rattling Almer’s right-post with a peach of a 25-yarder virtually from kick-off. This was at the end of some pinball passing between Birkir Bjarnason and Gylfi Sigurdsson that allowed Iceland to skate through their opponents.

It did not faze Austria and they were soon giving Iceland their own scare. Hannes Halldorsson dawdled in front of his goal over a clearance and Marko Arnautovic stole the ball and appeared to have a simple tap-in. But the forward slipped on the turf and the danger fizzled out.

Iceland’s callowness was to prove no hindrance. From a corner along the left Aron Gunnarsson, the captain, stopped the ball going safe with a header near the far post and in the ensuing scramble Austria were fortunate not to concede.

They were about to and this was from a classic throw-in move. Gunnarsson flipped the ball into the area, Kari Arnason applied a flick-on, and Jon Dadi Bodvarsson beat Julian Baumgartlinger to slide the ball past a wrong-footed Almer.

The blue section of the stadium may have been outnumbered by their red-shirted counterparts – there were around 10,000 Icelandic fans present – but the noise they made to celebrate the strike was deafening.

From here, though, the rest of this period was more or less controlled by Koller’s men. Arnautovic is one of those frustrating only on-his-day footballers. Thankfully, for Austria, this was one of them, as he posed a threat throughout. There was a pivot-and-shot with his left foot that Halldorsson clutched gratefully. He also bulldozed through the Icelandic rearguard before running out of grass. And, he turned playmaker on occasion.

When the first half ended Austria had dominated and, sloppily, spurned the chance to be on level terms. The referee, who had already turned away an Arnautovic appeal for a penalty, had no hesitation in pointing to the spot after 36 minutes when he saw Ari Skulason pull at Alaba’s arm as he jumped for a header. The left-back was booked but the defender Aleksandar Dragovic hit the post from the penalty and sank to his knees.

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Austria began the second half strongly. Arnautovic bent in a cross from the left and when the ball broke Alaba fired it at Halldorsson and Arnason cleared. Next, Skulason lived particularly dangerously. As a high ball dropped in the area he stumbled and then “accidentally” fell into Marcel Sabitzer. Up went the shouts for a second penalty, Koller ran along the touchline to add his voice, but the referee said no.

At the break Koller had brought on Marc Janko to play as the focal point, and Alessandro Schöpf, a midfielder, for the defender, Sebastian Prödl.

The ploy was to try to hit Janko’s height and pose Iceland a new problem.

But it was Schöpf who gave Iceland a question they failed to answer. From a central position and in true Ricky Villa-style, he weaved his way in and out of traffic, bamboozling the defence, before slotting home a terrific equaliser.

A pulsating contest took the next turn when Sigurdsson was handed a golden chance to put Iceland back ahead, following good work from Bjarnason, but he could not beat Almer.

Schöpf was proving an inspired replacement, the ball coming to him in space close-in but Halldorsson, not for the first time, was his side’s saviour.

Now, though, came an end to the game to remember.