Poland took a 17th-minute lead in Warsaw when Robert Lewandowski headed in Jakub Blaszczykowsk's superb cross from the right, before Greece's task was made even harder when Sokratis Papastathopoulos was sent-off just before half-time for two highly-debatable yellow cards.
Szczesny, though, gifted the Greeks an equaliser early in the second half when he failed to deal with a cross, allowing substitute Dimitris Salpigidis to stab into the empty net.
The Arsenal keeper was then red carded after brining down the Greece goalscorer, but substitute goalkeeper Przemyslaw Tyton dived to his left to keep out Giorgos Karagounis' penalty kick.
Neymar's move from Santos to Barcelona is no doubt the biggest summer transfer.
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.
Germany is one of the top teams ever and they will play the US on Sunday.
Jamaica is in need of a win against the U.S. Get the jersey of the Reggae Boyz.
The Nike Hypervenom is the latest cleat silo from Nike. It will change your game and is worn by the game's top players.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
The USA will wear their blue away jersey against Jamaica in their World Cup qualifier on Friday night.
England will debut their new away jersey against Brazil at the Maracana Stadium on Sunday. Get in the Gear