|Styliani Kaltsidou showed her all-around skills with a double-double of 20 points and 11 rebounds|
VICI Aistes came from 10 points down to lead in the final minute but Bourges recovered and scraped a 69-67 victory in Lithuania.
In a game Bourges desperately needed to win to enhance their chances of reaching the EuroLeague Women Play-Offs from Group C, Stella Kaltsidou scored 20 points and grabbed 11 rebounds.
The Kaunas club turned the ball over 19 times, leading to 21 points for Bourges.
Kiesha Brown had four steals for the visiting side.
All was going according to plan for Bourges, who nearly upset unbeaten Galatasaray last week in France.
They needed the victory at VICI Aistes to stay near the top four sides in Group C and started out well by outscoring the Lithuanian club 28-18 in the opening quarter.
Kaltsidou had 11 points in the frame.
Bourges were still in control at half-time with a 43-33 advantage and also with 7:53 remaining when Brown made a driving lay-up for a 62-50 lead.
With 4:54 to go, two Catherine Joens free-throws put Bourges in front, 64-53.
VICI Aistes finally made inroads in the last 3:30.
Vaida Sipaviciute buried a jump shot and Courtnay Pilypaitis scored seven straight points, which included a three-ball, before two Vita Kuktiene free throws even took the lead at 67-66 with 49 seconds to play.
The Kaunas outfit fouled Kaltsidou, who made two free-throws to put her side back in front.
Brown then split a pair for a 69-67 lead with 26 seconds to play.
Santa Okockyte, who had hit one of her two three-pointers in the game, launched another attempt with eight seconds to go but missed as Bourges claimed a narrow win.
VICI Aistes slumped to 1-6.
Bourges Basket head coach Valerie Garnier:
"It as a very important victory for our team in this competition because before this game we had only two wins. We new that Kaunas players are impressive shooters from the arc. At the end we tried to shoot to quickly and this was not a right solution when we had a 10 point lead in last quarter.
Bourges Forward Endene Miyem:
"It was a tough game, but we did our job. We made some mistakes at the end, we have to learn from this and try to not make mistake in other games."
VICI-Aistes Kaunas player Vita Kuktienė:
"We should have won this game, but made too many mistakes and gave our opponents too many offensive rebounds so the Bourges team made a lot of easy baskets."
Vici-Aistes head coach Mantas Sernius:
"I am very angry at my players because they didn't expect to win this game. Today the Bourges team did not play their usual game, so we just had to believe that we could win and take it. I hope our fans will forgive us because we always play for them."