Nyva Vinnytsia's best achievement in the Ukrainian Premier League was 10th place finish in the 1993–94 season. The club also surprisingly made the 1995–96 Ukrainian Cup finals, only to lose to Dynamo Kyiv. As a result, Nyva took part in the 1996–97 UEFA Cup Winners' Cup, even progressing to the First round after beating JK Tallinna Sadam on away goals (1:2 loss in Tallinn and 1:0 win in Vinnytsia). However, Swiss side FC Sion beat the Ukrainian side with a 6:0 score on aggregate (2:0 in Sion and 4:0 in Vinnytsia) ending the dream run in Europe.