Finland - ranked 32nd in the world - led comfortably throughout the encounter until Greece, who only recently fell out of the top 10, mounted a late fightback in vain.
Petteri Koponen and Lauri Markkanen starred for the Group A hosts with 24 and 17 points respectively, leaving their opponents to face a winner-takes-all clash with Poland in their final group fixture.
France join Finland in the last 16 following their 78-75 win against Poland, while table-toppers Slovenia beat bottom side Iceland 102-75.
Serbia, Latvia, Russia and Turkey will all play in the next round after Tuesday’s results in Group D.
Leaders Serbia beat Great Britain 82-68, Russia lost 84-69 to Latvia, and group hosts Turkey clinched their place with a 78-65 win against Belgium.
In Group C, Hungary followed up their first Eurobasket win since 1969 on Monday with another victory - this time over Romania to join Spain, Croatia and Montenegro in progressing to the knockouts.
Qualification in Group B is going down to the wire, with just a point separating Italy, Georgia, Israel and Ukraine. Lithuania and Germany are already assured of their place in the next round.
Georgia kept their hopes alive with a 104-91 overtime win against Israel in Tel Aviv.
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