The Poles, opening day winners over Serbia & Montenegro, didn't have a letdown against the Greeks who are already in next year's Olympics in Athens as hosts of that tournament, too.
Elzb Trzesniewska scored a game-high 18 points for Poland, who pulled away from a 31-31 half-time tie in the third quarter and led 54-43 goiing into the final 10 minutes.
Margo Dydek and Rena Piestrzynska each had 13 points in a winning cause.
Greece were led by Maria Samoroukova's 12 points while Aikaterini Deli chipped in 10.
Poland dominated this game on the inside, outrebounding Greece 48-33.
Dydek also blocked five shots.
Tomasz Herkt, Head Coach, Poland
"This was not an easy game for us, especially after playing Serbia and Montenegro yesterday. We had 48 rebounds and played good defense which was the key to the game.
Margot Dydek, Poland
"Greece have improved. They are a young team and they have very good guards. They shot the ball well but we managed to win in the end."
Giorgios Tsitskaris, Head Coach, Greece
"When we were shooting the ball well we had a chance to win the game. Poland was better than us under the basket. We played well for 25 minutes but our inside players got tired playing against Dydek."
"I agree with the coach. We are an inexperienced team and this is only our second appearance in a European Championship. I hope we can finish 4th in the group and qualify for the next round."