While the French outfit improved to 5-1 in Top 16 Group I, Den Bosch slipped to 2-4.
Telekom Baskets Bonn prevailed 67-59 at Belgacom Liege Basket to raise their record to 3-3 and joined Cholet in the Quarter-Finals.
Had Den Bosch triumphed, they would have progressed on a goal differential tie-breaker against Bonn but instead, their European campaign is over.
Rodrigue Beaubois made the big shots for Cholet at the end in the win over EiffelTowers.
Kees Akerboom's three-pointer for Den Bosch closed the gap to 66-65 with 2:34 remaining in the game, only for Beaubois to answer with a three for Cholet.
Anthony Richardson then replied with a jump shot for the home team with 1:54 to go and was fouled on the play.
He made the free throw to cut the deficit to 69-68, but Beaubois again hit a three-pointer to extend the lead back to four.
On their next possession, EiffelTowers missed two shots but grabbed the offensive rebound and called a timeout.
When play resumed, Cholet's Claude Marquis intercepted a pass to effectively seal the victory.
Beaubois and Marquis each had 18 points.
Richardson poured in a game-high 26 points for EiffelTowers.
Anthony Richardson, player EiffelTowers:
"We broke down defensively on occasions while they made their shots."
Erman Kunter, coach Cholet:
"I was surprised by EiffelTowers' intensity. We had to fight hard for the win. I am glad, because we are trying hard to get the momentum back in Europe."
Rodrigue Beaubois, player Cholet:
"Of course I was happy with my performance, but we needed the win as a team."