Belgium fell behind early but clawed their way back to edge Greece 58-56 in Group F.
Marjorie Carpréaux and Virginie Michiels each scored 12 points for the winners, with the former also finishing the game with five assists and six steals. Michiels, a 1.8m power forward, also had five rebounds.
Zoi Dimitrakou and Anastassia Gkotzi finished the game with 14 points apiece for Greece.
The Greeks stormed out to a 20-6 advantage late in the first quarter and were in 24-8 ahead two minutes into the second period after a pair of Dimitrakou free throws.
It was the perfect start, but one that Dimitirs Bakogeorgos' team was unable to build on.
The Belgians, who won their opening two games in the tournament but were then surprisingly heavy losers to Latvia, battled back and reeled off the last seven points of the half to trail 30-23 at half-time.
The Greeks stretched their lead to 35-25 with 7:24 to play in the third, however the rest of the quarter belonged to Belgium with Carpreaux sinking three of four free throws at the end to close to within 39-38.
Michiels' lay-up put Belgium in front at 42-41 early in the fourth quarter and they stayed in the lead for the remainder of the game, although victory was not assured until the end.
Elena Vlani made things especially interesting by making a three-pointer with 44 seconds to play to cut the Belgian advantage to 55-53.
Ellen Lauwers answered with a three-pointer for Belgium to restore a five-point lead but all Greece could muster was another three-pointer from Gkotzi - her second of the game.
In the other Group F contest, hosts Hungary lost for the first time, suffering an 82-55 defeat to Russia.
Elizaveta Rusakova and Tatiana Bokareva each had 12 points for the Russians, who grabbed a stranglehold on the game in the first half.
Russia built a 23-15 lead by the end of the first quarter and midway through the second were in command at 31-17.
Tatiana Bokareva's two free throws made it 39-22 at half-time and Kira Trzheskal marched to a comprehensive victory.