The Greek side took and early lead in the 2nd minute with Dimitris Limnios and doubled its goals in the 51st minute with Dimitris Siovas.
The home team reduced the deficit in the 82nd with Berisha but could nod avoid the defeat.
Greece, who plays next on 11th October with Moldova, leads its group with four points.
Meanwhile Cyprus is giving its second match this Wednesday morning (Australian time) hosting Azerbaijan.