Israel international Shay Doron poured in 23 points and American Laura Harper scored 19 while pulling down 18 rebounds for Besiktas as they ended up with three victories and seven defeats.
Nadezhda saw their EuroLeague season draw to a close with a 2-8 record.
The fans who showed up to watch the last game for both clubs in this season's competition were treated to a thrilling encounter.
The game was knotted at 56-56 heading to the fourth quarter and the lead changed hands on several occasions.
With 1:57 to go, the Russians went on top at 72-68 after Betty Lennox drilled a jump shot to take her points haul to 23.
Besiktas came right back with Milica Dabovic connecting from behind the arc to cut the gap to one.
On their next possession, Besiktas stayed with the hot hand as Dabovic hit another three for a 74-72 lead.
After Nadezhda's Anastasiya Veremeenko missed a potential game-tying jumper, the Russians fouled Besiktas and hoped for the best but Shay Doron sank two free throws and the Istanbul side claimed a four-point triumph.
Besiktas were just 10 of 17 at the line compared to Nadezhda's 20 of 26. They hit eight three-pointers to just six for the home side.
Besiktas were 21 of 56 inside the arc, while Nadezhda made only 17 of 46.
Besiktas, led by Harper, out-rebounded Nadezhda 47-39.
Aziz Akkaya, Besiktas Cola Turka coach:
"My players showed a lot of altruism in the game, though they were tired because of the long trip to Orenburg, but they hoped to win and they did it. Besiktas showed character and deserved the victory."
Yuriy Karandashov, Nadezhda coach:
"Not only players are guilty in a loss but the coaches toom, iff they could not turn the team's [fortunes] at the decisive moment. They (players) made a lot of efforts to take the lead but finally everything was decided at the last minute when Besiktas blocked some three-point shots."