Robert Lewandowski headed Poland into the lead before Greece's woes continued with the sending off of Sokratis Papastathopoulos before the break.
Goalkeeper Wojciech Szczesny fouls Greece's
Dimitris Salpingidis (R) [Photo:REUTERS]
Substitute Dimitris Salpingidis fired in the equaliser after the restart before he was brought down by Wojciech Szczesny, who was shown a straight red.
But Giorgos Karagounis's penalty was saved by substitute Przemyslaw Tyton.
It was a remarkable first match of the championship.
Poland frequently exploited their opponents' poorly defended left-hand side during the opening moments of the match.
The first goal threat came from that side. Lukasz Piszczek, who looked lively on the wing, beat his marker and delivered into the area. Star-man Lewandowski controlled and fed Ludovic Obraniak, whose shot was blocked.
Murawski was next to cause butterflies in the Greek defence when his shot was tipped over by veteran keeper Kostas Chalkias.
The breakthrough came in the 17th minute when Borussia Dortmund striker Lewandowski was left unmarked at the far post to head in Blaszczykowski's brilliant cross from the right.
Referee Carlos Velasco Carballo had let the game flow up until then, but shortly after the goal he showed the first yellow card of the tournament to Papastathopoulos, who appeared to fairly challenge for a header.
The Spanish official then delivered a huge blow to the Greeks when he brandished a second yellow followed by a red to Papastathopoulos.
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