The Polish outfit improved to 6-3 as Candace Dupree dominated with 18 points and 18 rebounds.
Wisla trailed 54-51 at the end of the third quarter but maintained their focus and three times the teams were level in the final period.
The crowning blow came with 3:20 left .
Laura Harper had just tied the game at 59-59 with a lay-up when Jelena Skerovic went to the other end and drilled a three for a 62-59 Wisla lead.
Besiktas had three opportunities to draw closer but Korana Zanze missed two jump shots and Tugba Tasci was off target with two free throws.
Slobodanka Maksimovic nailed a jumper to give Wisla a five-point advantage and they held on over the final 2:33 for a five-point win.
Besiktas (2-7) are eliminated from play-off contention.
Harper finished with numbers that were equally impressive to those of Dupree.
She had 19 points and 16 rebounds.