Zając previously played for Cracovia and Hutnik Kraków, before he moved to Polish powerhouse Wisła Kraków, where he experienced considerable success by winning two league titles and a call-up to the Poland national team. This saw Turkish side Denizlispor interested with his services, and Zając moved there for the 2001–02 campaign, however he only played in ten league games before returning to Poland with Zagłębie Lubin the following season.[1] With another chance to play in the Süper Lig, Zając joined Akçaabat Sebatspor in 2003, where he stayed for one season.[citation needed]
Halfway through the 2004 Chinese league season, Zając moved to Shenzhen Jianlibao to help them in their push for the league title. Achieving this, he remained with the team for the next five seasons despite the exit of most of their top stars and manager. When he left the team at the end of the 2008 league season, he became the team's longest serving foreigner. Zając remained in China and joined second tier side Liaoning Hongyun at the beginning of the 2009 league season and helped the team win the division title.[citation needed]