A lively, attacking game finished with both sides reduced to 10 men following the dismissals of Greek central defender Sokratis Papastathopoulos just before halftime and Polish goalkeeper Wojciech Szczesny midway through the second.
Greece fought their way back into the game having been outplayed by a rampant Polish side in the first period.
Striker Robert Lewandowski headed Poland ahead after 17 minutes, and the noise from over 56,000 home fans raised the roof which was somewhat bizarrely closed because of a storm earlier but with blue sky clearly visible above.
But Greece, showing the determination that took them to the title in 2004, equalised six minutes after the break and grew in stature as Poland allowed them more space and time to play.
Halftime substitute Dimitris Salpingidis forced the ball home after Szczesny misjudged a cross but worse was to follow for the 22-year-old keeper 19 minutes later when he tripped Salpingidis who had rounded him and was about to score.
Watch from Skai (in Greek) - Πρεμιέρα με ισοπαλία