Besok had a game-high 23 points and also pulled down 13 rebounds as his team claimed their third victory in the competition.
Both teams are now 3-2 heading into their final group game.
Galatasay controlled the opening half and went into the break with a 33-30 lead.
James Potter's three-pointer with seven minutes to play in the third quarter put Dexia in front for the first time at 44-42.
Both teams exchanged the lead before Antonio Graves nailed a three-ball to put Galatasaray in front for good with 13 minutes to go to make it 50-47.
Dexia kept the game close, however, and reduced the arrears to 70-67 with 2:25 on the clock, but the hosts hit back with a 10-0 run to claim a vital win.
Galatasaray had four players finish in double figures.
The Turkish outfit was superior shooting the ball on the night, making 20 of 38 (52.6%) inside the arc while the visitors were eight of 20 (40%).
Moreover, they committed just seven turnovers while forcing Dexia into 15.
Potter had 14 points and 10 rebounds in defeat.