This sort of thing doesn't happen any more. The globalisation of football, the manic cosmopolitanism of the game at the top level, the blanket television coverage of leagues from all over the world: it should all mean that there can be no glorious surprises like Armenia. And yet there they are, after three successive wins in which they have scored 11 goals, looking for a win in the Republic of Ireland to take second place in the qualifying group and a play-off for European Championship qualifying.

They have defied what Scott Murray once called the Josimar-Murdoch Law of Diminishing Returns, his theory that major tournaments are not what they once were because we have too much knowledge and there can never again be that thrill of realising a player or team we've never heard of is supremely talented.

Perhaps Latvia, who qualified for Euro 2004 by finishing behind Sweden in their group and then beating Turkey in a play-off (coming from 2-0 down with 24 minutes of the second leg to go, no less) are the last European minnow really to emerge, but they, like Slovenia before them, were a side based on dogged resilience. There's nothing wrong with that, of course, but sides who pack men behind the ball and look to nick one on the break are necessarily limited; they can only go so far and the fear must always be that they will end up, as Latvia did, making up the numbers in the finals itself, spending their three games looking to keep the score down and nothing else.

That's not to say sides should not look to defend themselves – Greece, after all, showed in that tournament what can be achieved by solidity and playing to your strengths – but a side based almost entirely on defence is necessarily restricted. And that is what makes this Armenia such a welcome surprise: they play proactive football that is very easy on the eye. They've got a long way to go before matching Greece's achievements (and they start at an even lower base), but in terms of style, Armenia are probably the most potentially exciting side to emerge since Denmark in the early 80s.

In that, this Armenia are true to the nation's traditions. Although there has only been an independent national team since 1992, in Soviet times Ararat Yerevan served as a de facto national side. Their greatest moment came in 1973 when they won an unexpected Double under Nikita Simonyan, who had already won the Double as a player and coach at Spartak Moscow. He was of Armenian heritage, and had essentially been exiled back to his homeland following disagreements with officials at Spartak.

"It was much harder to win the league with Ararat than it was with Spartak Moscow," Simonyan said. "We had some good players, but essentially we were a provincial side. I had to change my personal style, because the players had a different mentality. We had two Ukrainians in the side, but they had lived in Yerevan from childhood, so they had adopted the spirit of the people. Players from the south are more skilful, more technical, even if it is bad for the team as a collective. You have to stick them to each other."

That process of sticking the players to each other, of creating a cohesive unit in which they can express their individual ability, probably began under Ian Porterfield. The former Sunderland midfielder took charge in 2006, and oversaw 10 games before his death from cancer the following year. Although only two of them were won, what is significant is that only nine goals were conceded. The present coach, Vardan Minasyan, served as Porterfield's assistant, briefly taking over from him as caretaker.

"The results do not suddenly come out of the blue," said Armenia's Shakhtar Donetsk midfielder Henrik Mkhitaryan. "We have many young players who have earned the coaches' trust and have a clear understanding of what needs to be done. Our football is based on mutual trust between coaches and players. Everyone has the same approach, be it the coaches, the players, the Football Federation of Armenia or our team doctors. We are a whole and healthy mechanism.

"Our main strength is the team. Henrik Mkhitaryan would not be able to achieve anything alone. I am not myself without my team or my team-mates. It is thanks to the men I play alongside that I can show what I am capable of. So I am deeply grateful to my colleagues for their belief in themselves and in me. Together we are striving towards one goal."

Porterfield may have begun to change the mentality, but what has really elevated Armenia is the emergence, in the past year (and it really is only in the past year; when the Republic of Ireland won 1-0 in Yerevan in their first game in qualifying nobody thought it might prove a key result) of a highly gifted young generation of players. Although the goalkeeper, Roman Berezovsky, is 37 and the right-back and captain Sargis Hovsepyan, is 38, the rest of the squad are in their early-to-mid-20s.

That, in part, may explain why so many of the squad still play in Armenia, or at smaller clubs in Ukraine. Five of the side that beat FYR Macedonia 4-1 on Friday still play in the domestic league, which is ranked 50th best in Europe by Uefa, above only the Faroe Islands, Andorra and San Marino. Only Mkhitaryan is at a club that has even come close to Champions League qualification.

He is likely to be vital on Tuesday, and not just because he is Armenia's best player. Minasyan, who cites Barcelona and Arsenal as his models, favours a 4-2-3-1, and pace in wide areas has been a feature of their recent matches. Given Ireland's sluggishness at full-back that could be decisive, but the question Minasyan must answer is whether to use Gevorg Ghazaryan on the left and Mkhitaryan on the right, or to pull Mkhitaryan back into a deep-lying creative role and explore other options – the former Ajax forward Edgar Manucharyan perhaps – wide. Is it better to pack strength on the flanks, or to ensure the supply to the flanks is good?

Playing Mkhitaryan wide perhaps strengthens Armenia defensively, allowing them to play a ball-winner alongside Karlen Mkrtchyan at the back of the midfield. While this is a side of far more attacking ability than Porterfield's, the additional expressiveness has come at the cost of some of the defensive resilience of old. "Armenia will give Ireland chances but they are also capable of taking their own – as we discovered to our cost," said Martin Skrtel, whose Slovakia side lost 4-0 to Armenia last month.

"We created enough chances but we weren't able to score. We still have a young team, though, so we have to retain perspective. The one thing I would say to any team playing Armenia is to make sure you score against them. We didn't do that in the first half in Zilina and then we went and conceded four goals after the break. There will be chances in the game, no doubt about that. And Ireland have got to make them count."

As Russia showed in the first half in Dublin, though, Ireland can be left befuddled by teams who move the ball at pace. Then again, as Ireland showed in the second half of that game, the direct approach can unsettle even the most poised sides. In a sense, anyway, the most important thing is that Armenia are there with a chance of qualifying at all, not just for their players and fans, but for all minnows. Their progress is a message that dull solidity is not the only way for the minnow.