A lively, attacking game finished with both sides reduced to 10 men following the dismissals of Greek central defender Sokratis Papastathopoulos just before half-time 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.
Half-time 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.
Spanish referee Carlos Velasco Carballo showed him a red card but, with the fans jeering and whistling, the first thing replacement Przemyslaw Tyton did was save Giorgos Karagounis's penalty, diving to his left and parrying it to safety.
The only other time there had been multiple dismissals in the opening game was in 1976 when Czechoslovakia played Netherlands and three players were sent off.
"I've told the players to cheer up, it would be much worse if we lost the game," said Poland coach Franciszek Smuda.
"We should not concentrate on this. There was a lot of pressure on my very young team, we did not have the experience of the Greek side."
Salpingidis added: "We got off to a very bad start, were a bit unlucky but we managed to turn it around because this team has soul and our Greek soul is above football, it is above everything."
RESIGNED LOOK
Greece scored a penalty when they beat Portugal 2-1 in the opening match of Euro 2004, but a repeat of that scoreline would have been unfair on the Poles, who started well but allowed their opponents to dominate in the later stages.
The resigned look on Smuda's face at the final whistle said it all. He knew his team had blown their chance of a first ever victory at the finals after wasting almost all their chances in a one-sided first half when Greece were dreadful.
The opening stages, though, gave little indication that the end result would be anything other than a Polish victory.
With Lukasz Piszczek overlapping down the left, skipper Jakub Blaszczykowski having the freedom of the right and Ludovic Obraniak forcing his way through the middle, Poland were in complete control.
Lewandowski, the third-highest scorer in the Bundesliga this season with Borussia Dortmund, had two sniffs of goal before opening the scoring when he powerfully headed home a cross from Blaszczykowski with Greece keeper Kostas Chalkias floundering.
Defender Damien Perquis shou
