The Greek team wrote their first win in the Qualifying Round when they outscored Ukraine 90-61 in Group E.
Greece now holds a 1-3 record in the group, while Ukraine dropped to 0-4.
Both teams still hold a chance to play the 5-8 Classification Round but Greece obviously has the better chances.
Linos-Spyridon Chrysikopoulos led Greece with 21 points, eight rebounds, five steals and three blocks, followed by Georgios Mavrogiannis with 15, Spyridon Motsenigos with 13 and Panagiotis Papoulias who had 11.
Olexandr Mishula and Oleksandr Prokopenko scored 12 each and V'Yacheslav Bobrov had ten with nine rebounds for Ukraine.
"If we had played yesterday with this passion and commitment we wouldn't have lost by 30 points to Lithuania," said Nikos Toufas after the game.
"Today we played better and showed the talent that we have on the team."
Right from the start it was clear who's the boss on the court when Greece took a double-digit margin already in the first quarter.
Ukraine never found the path back and will pray for their first win to arrive tomorrow.
Coach Toufas started with Chrysikopoulos on the bench and when he got his first minutes on the floor came the change.
The long guard right away stole the ball at half court to finish with a big dunk and later added four more points on the way to a 23-12 Greek lead.
Greece held a 27-15 lead already after ten minutes in the game, and showed dominance in every aspect on the floor.
Ukraine scored seven points in a row thanks to Mishula but Greece was ready to hit back, and with an 18-4 run wrote a 21 point difference at half time, 47-26.
The second half allowed Chrysikopoulos and Mavrogiannis to improve their stats and their team to increase the lead.
"Mavrogiannis, our shooter, got injured in the game and I hope he will be fit for tomorrow," added Toufas thinking already about what's expecting his team the next day.
Greece will face Spain on the closing day of the round as Ukraine will face Serbia.