Former Brazil international center and Halcon Avenida player Alessandra had 21 points and 15 rebounds for Bourges in a dominating effort.
Cathy Melain (14pts) and Endene Miyem (10pts) also reached double figures for the French giants, who won the battle of the boards 37-22 and held Avenida to just two of 11 shooting on the night from long range.
Anke De Mondt, the Belgian international, hit one of those three-balls and had 13 points to lead Avenida.
Latvia international Gunta Basko had nine points for the Spanish team which is now 6-3 with Bourges and Wisla Can-Pack Krakow.
Bourges went into the contest expecting a hard game after falling in the first encounter between the sides 77-70 in Salamanca.
Pierre Vincent's team led from start to finish and had a 26:11 lead two minutes into the second quarter.
A Basko lay-up left Avenida behind at 44-29 at half-time but they wouldn't mount a challenge after the interval.
Alessandra scored the first basket of the third quarter and Melain followed with a three-ball to put Bourges on their way to a decisive triumph.
José Hernandez, coach Halcon Avenida:
"Bourges were too strong tonight. It was a tough game inside and Bourges won the rebounds. Our two American players were ill during the week so it was hard to perform our fast game although this is not the reason for our defeat. Alessandra was strong tonight and when you have to face a strong player in the ideal [for her] conditions it's impossible to come back."
Pierre Vincent, coach Bourges:
"The most important was to win and to win by more than seven points. In EuroLeague, the games are more tactical, we played on the weaknesses of Salamanca when they put two smaller players inside. When Salamanca came back during the game, some players were nervous, we have to learn to be calm in these moments. After the game in Salamanca, we studied a lot, tonight we stole a lot of balls, we defended hard and we did not let the other team to take any easy shots. We played clever."