The Polish outfit prevailed 86-62 to leave both sides with 3-5 records in Group C.
Alana Beard had 22 points and eight rebounds and also came up with four steals for Lotos PKO BP, who reeled off the game's first seven points and stayed in front for the entire contest.
Leading 46-41 early in the second half, Lotos PKO BP went on a 12-3 run to take a firm grip on proceedings.
Ivana Matovic had six points in that spurt and Beard four.
Lotos PKO BP got a lift from Monique Currie, who drilled four of five shots from long range and finished with 19 points.
Coach Jacek Winnicki had no complaints with his team's effort at the free throw line where they made 16 of 21 (76.2).
Union Hainaut Basket of Valenciennes, France, took far less trips to the charity stripe and made seven of 10.
The Lotos PKO BP three-point shooting was also superior. They were eight of 17 (47.1%) while Union Hainaut were five of 16 (31.3%).
Sabrina Reghaissia had 11 points and Vedrana Grgin Fonseca 10 for Union Hainaut.
Tiffany Stansbury also contributed eight points and eight boards for the French team.
Fabrice Courcier, Union Hainaut Coach:
"It wasn't a good match of our team. We wanted to win but Lotos PKO BP played a very strong defence, also their percentage from the field was high. Now our situation is difficult because we play our last two games against Ros Casares and UMMC Ekaterinburg."
Jacek Winnicki, LOTOS Coach:
"We had to win this match and we did it. We made one step more to the next round but we are still far from that. We must win in Sibenik - it's going to be the most important match during the season. Thanks for my girls and to the fans."