The Italians, in winning for the fifth time in seven games, stormed into a 21-13 lead by the end of the opening quarter and effectively had victory in the bag by half-time when they had a 48-27 stranglehold on proceedings.
Mudju Ngoyisa had 18 points and Laura Macchi 15 for the Schio club, which out-rebounded ESB Lille Metropole 43-29.
Sandro Orlando's side was 24 of 46 inside the arc and six of 14 from long range.
ESB were nine of 29 from two-point range and 12 of 29 from the arc.
The Schio triumph would have been more comprehensive had they shot better at the free-throw line where they made just nine of 18.
Wisla Can-Pack Krakow will reclaim top spot in the group after their game at MiZo Pecs on Thursday.
"We did not play [well] at all in the first half. It's too bad because we came back in the second one but it was too late. Schio started the game perfectly, with a 14-0 run. Our players need to show more determination."
Sandro Orlando, coach Beretta-Famila Schio:
"I want to congratulate Abdou for this game. This is never easy to play with such a young and inexperienced team . Also I have the feeling that Tanqueray, their young point-guard is playing better and better."