Having enjoyed a 94-62 rout at home in Russia on Tuesday, UMMC found things much harder going on the road and had to survive two late Fener misses to hang on to their lead.
UMMC had trailed 64-58 after Nevin Nevlin's jump-shot 6:36 from time in the final quarter.
But former Fener star Cappie Pondexter began the fightback as she sank a three-pointer before drawing a foul and heading to the line to make both her shots.
That closed the gap to one, and Nevlin then fouled Deanna Nolan to give UMMC another chance from the charity stripe, with Nolan duly obliging to make it 65-64 to the visitors.
Fener grabbed the lead back on Nevlin's jump-shot but when Nolan made a lay-up 3:39 from time, UMMC were ahead for good.
Pondexter made it a three-point lead with another lay-up, and Nevlin missed a three-pointer that would have tied it.
Tammy Sutton-Brown's lay-up cut the lead to one with 2:12 to go.
A scrappy finish then followed as Penny Taylor missed a three-pointer for UMMC before Tuncluer and Nevlin each missed a pair of chances as Fener watched the game slip through their fingers.
The chance to win it was still there after Taylor could only split a pair of free throws 24 seconds from time, but Nevlin missed a jump shot with five seconds left and Birsel Vardarli was off-target with a three-ball with two seconds on the clock.
Pondexter had 17 points to lead UMMC while Sandrine Gruda had 14 and Nolan and Maria Stepanova collected 12 each.
Sutton-Brown's 14 points led Fener, while Nevlin and Nevriye Yilmaz had 12 each and Vardarli finished with 11.