The result has dropped Wisla to 0-2.
Jose Ignacio Hernandez's Wisla trailed, 51-40, 2:30 minutes into the fourth quarter but point guard Cristina Ouvina scored to ignite a 9-1 run that was capped by Justina Zurowska.
Györ kept their noses in front but a missed free-throw then proved costly.
Krisztina Raksányi made just one of two attempts at the line with 10 seconds remaining to give her side a 58-55 lead.
De Mondt punished her for the miss at the other end with a three-ball from way out for Wisla to force the extra period.
Zurowska hit a jumper to put the home side in front but Chalysa Shegog leveled the contest and then two Natalie Hurst free-throws put the visitors in front again.
Ouvina knotted the game again at 62-62 with a pair of free-throws but jumpers from Zsófia Simon and Nora Nagy-Bujdosó put the Hungarian outfit back in front to stay.
Dora Horti had a game-high 23 points and 13 rebounds in defeat.