Daniel Larsson grabbed the only goal of the third qualifying round first leg tie after 18 minutes, leaving the Scottish champions with a major hurdle to overcome in next week’s away leg.
It was another frustrating encounter for Ally McCoist, with the new Rangers manager still to secure his first competitive win at the Light Blues helm.
McGregor, Bougherra, Weir (Juanma Ortiz 29), Papac, Whittaker, Davis, McCulloch, Edu, Wallace, Jelavic, Naismith.
Melicharek, Halsti, Jansson, Andersson, Hamad, Mehmeti (Amin Nazari 54), Mutavdzic, Pekalski, Durmaz, Figueiredo (Rexhepi 69), Larsson (Yago 81).
Ref: Antonio Lahoz (Spain).