Cristhian Stuani had a long way to run: up and over the advertising boards, across the vast, empty space between him and the Girona fans, beyond the Barcelona badge covering the void to the stand, somewhere in the distance. Way back there, at the top of Montjuïc, you really can’t see much but what little they could see was as good as it gets, and now the greatest icon of all was coming into view. A couple of minutes before, 3-1 up, the 350 or so supporters who had made the 99km bus journey south had been busy meeting every pass with an “olé” only for a late goal from Ilkay Gündogan and an even later chance for Robert Lewandowski to put the fear back into them, but now they could really let loose.

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It had actually happened. The Uruguayan, 37, had just scored his fifth in seven days, and was heading for them, teammates following close behind. The clock on 94.34, his volley had won perhaps the best game of the season so far, making the score 4-2 and the victory secure. For the first time in their La Liga history, Girona had beaten Barcelona, the team most people in their town tended to support until now. Which may not be as dramatic as it sounds – although founded in 1930, their first division history is only three and a half years long – but which makes it even better; it also means they will get to try again. “I think we’re mathematically safe,” said their coach, Michel Sánchez.

Previously at Rayo Vallecano and Huesca, where he suffered relegations and celebrated promotions, Sunday night was Michel’s 100th primera game; it was also, he said, his best, celebrated by embracing his players, a look of incredulity on their faces as they danced in a circle. “The mother of all victories,” one local paper called it. Beating Barça took Girona over 40 points and to survival. The club that only made it to primera in 2017 and went down again two years later, whose budget is 14 times smaller than Real Madrid’s, less even than bottom-placed Almería, will now reach their fifth year as a first division team. Objective secure, it is time to set another one. Like: winning the league.

Like, really: winning the league.

At the start of the season, one of those glorious guidebooks that Spain’s sports papers produce, a bible for the one true faith, declared that Girona were looking to “make history” – by reaching a third consecutive year in primera. Another one set their target as first division “consolidation”, getting the points needed for survival “as soon as possible”, and living a “tranquil season”. Turns out that “as soon as possible” was with 22 weeks to spare, and as for tranquil, forget it. Before Sunday’s game, Michel had insisted that a win against Barcelona would take Girona into “another dimension”; it also took them top, two points clear of Real Madrid, seven above Atlético and Barcelona. The history they’re making is bigger than anyone dared imagine.

This wasn’t supposed to happen, not even with Girona being owned by Manchester City, who have 47% of the shares. Although City provide stability and knowhow, active in structural organisation and sporting planning, right down to conversations between Michel and Pep Guardiola; much as that may remove some of the romanticism of a club from a place with a population of just over 100,000 achieving this, their success is not so easily explained. Theirs is not a squad of City players – only Yan Couto and Savinho belong to the City Football Group – and nor are they spending City-type money. La Liga’s rules won’t allow it. The first-team budgets they set place Girona 14th.

Look at the starting XI against Barcelona and only three cost anything, the total outlay under €15m. They didn’t include on-loan Barça midfielder Pablo Torre as €300,000 in penalty payments to play him, Michel said, is “a lot of money.”

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Daley Blind came from Bayern, but they didn’t want him. While Xavi complained that on-loan Eric García could face his parent club, it’s not like Barcelona had tried to keep him either. Miguel Gutiérrez is a Real Madrid player, but a 22-year-old academy product with no obvious place there yet. CFG-owned, Savinho was at Troyes, but had been demoted from the first team. Aleix García came from Eibar where he had been relegated and Iván Martín from Alavés having suffered the same fate. Between them, Girona’s squad have experienced 38 relegations, far more than their titles won. In the summer, they lost top scorer Taty Castellanos, Rodrigo Riquelme, Santi Bueno and Oriol Romeu, who went to Barcelona for €3.5m. “They’re not doing us any favours,” part-owner Pere Guardiola lamented, but no one could begrudge Romeu his move up.

In short, this isn’t where they were supposed to be, not this late. When Girona first became leaders in September, Michel said the problem was it was week seven, not week 38. They had not yet played the biggest teams and the following Saturday, as if to prove the point, they lost 3-0 to Real Madrid. But nine more matches have passed and they’re still there. It is December and Girona are top, Gutiérrez saying: “Well, let’s see how far it takes us.” Even if that’s not to the title, the team that has never been into continental competition has a 12-point cushion in the Champions League places, 17 over the last likely European place, which is extraordinary enough. Only that’s not enough. “Just” a Uefa place, their new, publicly stated target, would feel like it falls short now.

When Girona played Madrid, defeat reinforced the idea that their good run could be dismissed. They hadn’t yet played or beaten the best teams – they had drawn with Real Sociedad – and were defeated by Madrid. It is true, too, that they are still to face Atlético or Betis, and that they drew with Athletic Bilbao, meaning Sunday’s victory over Barcelona was their first against a top-seven side, reasons perhaps to be reluctant to see them winning the race. La Liga’s “supercomputer” still only rates their chances of being league champions as 2.3%.

And yet that 3-0 flattered Madrid, didn’t sink Girona, and they won seven of the next eight. It’s 16 weeks now and they’re not top because the leadership is cheap. They have 41 points: 13 wins, two draws and one defeat. Only Madrid, Barcelona and Atlético have ever reached this stage with so many, their points projection 97. And while they have picked up 19 points having trailed, those comebacks aren’t epic or luck, they’re logic. They have won seven in a row at home and are only the second team to beat Barcelona, after Madrid. They put four past them, for goodness sake. There were four more against Granada and Osasuna, five against Almería and Mallorca. This was a “recital from a leader with no limits,” ran the cover of Marca. “Girona rule here,” said AS. “Girona are serious”, said both of them, and indeed everyone else. This was the new dimension. “An assault on power,” L’Esportiu called it.

Not that it had been easy. For the first 20 minutes, Eric García said, Girona had felt “asphyxiated”. Aleix García admitted they had looked around and thought “how are we going to rob a ball here?” But that only makes it better. Michel had warned them that they had to be ready to suffer, that the domination they were used to would be denied them but that they must find a way through, their way; they had to have the personality to make Barcelona chase. To draw them in, commit them, and play. And that’s the thing; Girona are not just Spain’s best team statistically, they are the Spain’s best team, full stop.

From a sharp, incisive move in behind the right-back, Barcelona cut open in three touches, Artem Dovbyk gave Girona the lead. A Robert Lewandowski header made it 1-1, but Gutiérrez, a full-back who isn’t really a full-back, scored a superb second. It was open, it was fun, and it went from end to end – “we took 31 shots,” Xavi noted, not entirely unjustly – yet it also felt like it was also closer to what Girona wanted than what Barcelona did, and they scored the third with nine minutes left through Valery Fernández, “olés” following soon after. Michel had “set up a rondo at Montjuïc,” one headline claimed. When Gündogan made it 3-2, García admitted wondering if the win would slip away, but a free header from Lewandowski, who last week got one on the nose, hit his shoulder on 92.36. And then on 94.34, there was Stuani, volleying in and heading towards the fans, Barcelona beaten.

The way Girona have beaten others. They have scored 38; across Europe’s five top leagues, only Bayern Munich and Bayer Leverkusen have more. Two of the three players to play the most passes in La Liga are theirs – Aleix García and Blind – and no one has built more goals than them; these aren’t set plays or fortunate rebounds. In the week before the game, Aleix García admitted he would like to go to Barcelona; after it, the sporting director, Quique Cárcel, joked: “I asked him if he still does: he says he’s staying.” On this evidence, of course he is. Asked if Girona were the best team he had seen, Xavi replied: “Yes, no doubt.”

“We saw a good side … and one that wants to be,” Michel said, only for the Barcelona coach to turn that upside down, describing Girona as the a team who are “a bit like what we want to be”, one that “is brave, presses, doesn’t just boot the ball”. One, above all, that is top of the table and playing the finest football in Spain.

Barcelona 2-4 Girona, Cádiz 1-1 Osasuna, Atlético 2-1 Almería, Mallorca 1-0 Sevilla, Villarreal 0-3 Real Sociedad, Real Betis 1-1 Real Madrid, Alavés 0-1 Las Palmas, Getafe 1-0 Valencia.

Monday: Granada v Atheltic Bilbao, Rayo Vallecano v Celta Vigo.