 She can also play as a field player, and while playing for Energiya Voronezh she scored a hat trick over KFF Shkiponjat in the 2005 UEFA Women's Cup.Zvarych took part in the UEFA Women's Euro 2009 as Nadiya Baranova's reserve.With Ukraine eliminated she was a starting player in the final group stage game against Finland, but she had to be replaced five minutes before half time following a collision with Laura Kalmari.