If it carries on the way it started, Euro 2012 will be an absolute cracker. For that we have to thank first the players of Poland and Greece, who set aside the tradition of the safety-first stalemate with which major football tournaments so often begin and instead hurled themselves into a maelstrom of non-stop action before emerging with a 1-1 draw that did credit to both sides. Then came Russia, crushing the Czech Republic in Wroclaw, their 4-1 victory topped off with a virtuoso effort from Roman Pavlyuchenko. The former Tottenham Hotspur forward came on to score a goal that in three weeks' time is likely to find itself in contention for the tournament's finest.

None of the anticipated caginess, then, in either Polish stadium, and now the attention switches to Ukraine, the tournament's other co-host, where the teams in this evening's two matches, Holland versus Denmark in Kharkiv and Germany versus Portugal in Lviv, will be expected to maintain the standard of entertainment.

If the opening match in Warsaw was by no means the sort of elevated affair that would have Uefa's technical committee drooling, it demonstrated that such contests do not have to be particularly sophisticated in order to be compelling. After Poland had started confidently and taken a deserved lead, Greece went down to 10 men before regrouping at the interval, mounting a terrific comeback which might have ended in triumph had their captain, Giorgos Karagounis, not seen his penalty attempt saved by Poland's substitute goalkeeper, Przemyslaw Tyton, after Wojciech Szczesny had been sent off.

A howling climax saw the two sides, both down to 10 men, miss presentable chances, the crowd's response amplified by the closing of the retractable roof over the fine new stadium erected for this championship.

Earlier it had echoed to the sound of an anthem specially composed for the tournament. Here's how it goes: "Hei! Koko koko Euro spoko / Pilka leci hen wysoko / Wszyscny razem zaspiewajmy / Naszym doping dajmy." And here's the translation: "Hey! Cluck cluck Euro's cool / The ball flies up so high / All of us, singing together / And cheering our boys." That "doping", incidentally, is Polish for "cheering". A later verse mentions Poland's head coach – "Our brave boys / Are in white and red / They will win it / And Smuda will be happy".

Franciszek Smuda was indeed happy after the first half of last night's opening match, in which his players responded to the fervour of their supporters by launching wave upon wave of attack down the left flank of Greece's defence until in the 17th minute Robert Lewandowski, a Warsaw boy, was able to score the first goal of the tournament.

Poland's cause was helped when Greece's central defender Sokratis Papastathopoulos was harshly sent off for a second yellow card a minute before the interval. But Greece equalised through a substitute, Dimitris Salpingidis, early in the second half and even had an opportunity to take the lead with 20 minutes to go when Szczesny left the pitch without protest after tripping Salpingidis inside the area. To a mighty roar from the ranks of white and red, Tyton parried Karagounis's kick.

And it had all started so gently, with a pleasant little opening ceremony that included dancers, ribbons, and a pianist performing a Chopin etude to a thunderous beat supplied by the turntables of an Italian DJ. But a match between two modestly talented sides turned into a genuine thriller, full of chances and drama and, in the end, screeching tension for Smuda and the home supporters.

The Greeks, descendants of the defensively obdurate champions of 2004, would not have been inclined to put much faith in their rearguard after their display in the early stages. Before Lewandowski gave his side the lead, the visitors had already endured persistent torment down the left flank in particular. The opener arrived after Jose Holebas, Greece's left-back, surrendered possession inside his own half and was helpless as Jakub Blaszczkowski sent over a deep cross that offered Lewandowski the opportunity to head into the empty net.

Holebas, born in Germany to a Greek father and a Uruguayan mother, had been given such a mauling that it was something of a surprise to see him re-emerge after the interval. Instead the crucial half-time substitution involved the arrival of Salpingidis, the 30-year-old PAOK striker who made Greek football history in a World Cup group match against Nigeria in South Africa two years ago when he scored his country's first goal in the finals of the competition. On Friday night he shot home after a misunderstanding between Szczesny and one of his defenders.

Smuda had picked a starting line-up including several of his "Plastic Poles", a group of players born in France and Germany and enticed to acquire Polish passports in order to reinforce the Eagles. The policy has been criticised by some of Smuda's compatriots, including Jan Tomaszewski, the goalkeeper who denied Alf Ramsey's England a place in the 1974 World Cup.

The head coach insists he is building a youth-based team who will be ready for Brazil in two years' time, and there were signs last night that, after Polish football's long, dark night, he may be making progress, with the 23-year-old Lewandowski as his star turn.

But Greece, delighted by their comeback, celebrated the draw as if they had won the Henri Delaunay Trophy all over again, while Russia, who beat Italy 3-0 in a warm-up match last week, confirmed the view of those who regard them as the tournament's dark horses. What a start: now we shall see if Robin van Persie, Christian Eriksen, Cristiano Ronaldo and Mesut Ozil can live up to it.