Slavia were one goal down just two minutes into the game after Hunter scored following a corner.
Slavia failed to score quick equaliser with several decent chances during opening 20 minutes.
Eventually the red-whites managed to equalise on 36th minute by Tereza Kožárová.
It took less than 5 minutes for Kožárová to score her second of the night and give Slavia deserved lead.
Shortly before the break, Jarchovská added third with a beautiful effort from outside the box.
Slavia set the pace of the second half and Kožárová completed hat-trick on 75th minute.
Second Leg will be played in Prague at Sinobo Stadium on Wednesday 25 September. KO at 6:30 pm.
Fife – Notley (82. Leishman), Hunter, Murray, Michie – Boyle, Cornet, McGregor (82. Higgins), Gallacher – Cavanagh (61. Davidson), Napier
Lukášová – Jarchovská, Necidová, Pincová, Blackwood – Divišová (70. Szewieczková), Svitková, Bartovičová, Persson, Khýrová (82. Veselá) – Kožárová (89. Černá)