Evina Maltsi scored 23 points and point guard Dimitra Kalentzou 21 as the most unheralded of national sides at the EuroBasket Women beat Slovakia 64-59 on Friday.
Greece, beaten in all three games they played two years ago when the competition was staged in Italy, will on Saturday have a chance to qualify for the 2010 FIBA World Championship in the Czech Republic when they play in the fifth-place game.
They will face the winner of Latvia's Classification Round clash against Italy.
Greece coach Kostas Missas, who is playing to rave reviews in Latvia for his tactical nous, managed to get his team focused on the Slovakians after Thursday's 51-49 defeat to France.
Had the Greeks won that game, they would have played in a Semi-Final and qualified for the Czech Republic, and the EuroBasket in 2011.
"We said nothing after the defeat to France," Missas said.
"This morning we spoke about forgetting everything that happened before.
"We must find our hearts and soul in this game. Defense, it was the main thing that gave us the opportunity to win this game.
"Defense keeps you from losing the game while offense gives you the ability to win the game."
Greece held Slovakia to 36% (24 of 66) shooting from the floor and also forced them to commit 19 turnovers.
One big difference in Friday's win was Greece's ability to not only get to the charity stripe but to make those free-throws.
They were 27 of 32 (84%) for the contest while Slovakia were seven of 10 (70%).
Greece's Styliani Kaltsidou said: "It was a very difficult game.
"We found the heart and soul to play this game.
"Now We must forget everything and we must be focused on our next game that for Greece national team would be a great success if we were to win."
Missas knows the stakes are extremely high for his team on Saturday.
"We don't have much time to recover but we must again find more heart, more patience for a very difficult game that is coming up," he said.
"Latvia is a very good team and they play at home so I'd rather play against Italy.
"But every game you play, you must stay in the plan. I expect for the last game of this tournament for my players to show more confidence on offense and leave defense to me."
Defeat was a bitter pill for a much improved Slovakia team to swallow.
They had failed to even qualify for the EuroBasket Women in 2005 and 2007, but had the look of a team early on in the tournament that could capture a medal.
They have endured three straight defeats. Pokey Chatman's team fell to Greece 59-57 in their last Qualifying Round game and then lost a heart-breaker in the Quarter-Finals to Belarus, 70-68.
"Congratulations to Greece for a fine performance in terms of their aggressiveness," Chatman said.
"I think from the beginning, they gave themselves an opportunity to win this game.
"Greece shot 32 free throws because they were aggressive and they attacked the basket, we only had 10.
"Greece didn't look tired today so credit to them."
Slovakia will take on the loser of Latvia's game with Italy.