The Polish side’s Ukrainian midfielder Vladyslav Kochergin scored the first goal of the match at the Municipal Stadium in the southern Polish city of Częstochowa in the seventh minute, and Fabian Piasecki doubled the score from a penalty in the 63rd.
South African Mihlali Mayambela scored for the Cypriot team in the 88th.
Raków will play Aris in the second leg next Tuesday, August 15, in Limassol, a city on the southern coast of Cyprus.
The winner of the two matches will go on to face either Danish side FC Copenhagen or the Czech Republic's Sparta Prague in the fourth and last round of Champions League qualifiers, Polish state news agency PAP reported.
Raków in May won the Polish premier league championship for the first time, while heavyweights Legia Warsaw, the most successful Polish football club in history, finished runners-up.
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Source: IAR, PAP