Petr Cech joked that the caveman look may frighten his children and his Czech Republic team-mates are in the same offensive territory but they will gladly run the risk. The Czechs have taken a no‑shave-until-we-exit pact. The hairier they get at Euro 2012, the happier they make their nation.

The Czechs are doing things differently. They won their opening matches at the 2006 World Cup and the previous European Championship only to fall short of the knockout stage. This time they crashed 4-1 to Russia in their first Group A fixture yet, after shattering Poland on Saturday night, they have qualified on top of the pile.

"Opening games never win or lose you the tournament," Cech said. "We've experience of that from the past. It was a pity that we put ourselves under huge pressure after the Russia match and with the goal difference as well. But we did really well against Poland. We were much the better team."

It was not the case for the first 30 minutes when, overdosing on adrenaline in front of a giddy home support, Poland called the tune. They created the chances to have advanced to their first European Championship quarter-final but they missed them. Cool and calculating, the Czechs played the long game. When they learned that Greece had scored late in the first-half against Russia, meaning that victory rather than simply a draw was essential, they raised their level. They controlled the second half and Petr Jiracek's goal was their reward.

The margins were slim. With virtually the last act, Michal Kadlec flung himself to clear Jakub Blaszczykowski's shot. Had the Poland midfielder scored, it would not have saved his country but it would have eliminated the Czechs. Kadlec's heroics will live long in the memory.

The Czechs have been on the wrong side of late drama and Cech, in particular, was scarred by Euro 2008. With three minutes to go in the final group game against Turkey in Geneva, his team led 2-1 and were bound for the quarter-finals. Yet Cech, inexplicably, fumbled Hamit Altintop's cross, which allowed Nihat Kahveci to equalise. In the very last minute, Nihat scored again to propel Turkey through.

Cech was pilloried in the Czech press. "I was responsible for losing against Turkey," he said at the time. "It was my mistake which really changed the game." It made the triumph over the Poles taste even sweeter. Cech had been at fault for the goal that his team conceded in the 2-1 win over Greece, having fumbled another cross but against Poland he stood tall in the face of the early onslaught.

Wroclaw had hoped to stage an epic party. Almost from dawn, the cries of "Polska" could be heard. Bands marched through the streets; faces daubed in red‑and-white radiated excitement. When Poland started at pace, the atmosphere was feverish but the scene in the small hours told its own story: empty glasses littered the deserted fan-zone; the locals were subdued.

The glory belonged to the Czechs and they have begun to dream. Milan Baros, the former Liverpool striker, found himself asked about some game in Istanbul. More than most players, he knows that anything is possible.

"The Champions League final in 2005 is still the pinnacle for me but maybe we're going to beat that," Baros said. "We still have three games in front of us. We know that the quarter-final will be tough but it's a play-off, you never know. It's about one set piece, it's about one chance. We have to play as we played against Poland and, hopefully, we will go through to the semi-finals."

Cech and Baros are getting itchy, for more than one reason. "We said that we wouldn't shave until we go out of the tournament," Cech said. "I don't know whose idea it was … it was a team decision. It's for the team banter. I last shaved on the first day we arrived so it must be two weeks. I hope I'm not going to scare my kids too much but I don't mind if I have it until 2 July. I don't mind at all."