Striker Benni McCarthy opened the scoring on 29 minutes and Matt Derbyshire sealed victory with a second goal for Rovers ten minutes from the end of the game in Lithuania.
Rovers: Friedel, Ooijer, Nelsen, Samba, Warnock, Bentley, Tugay, Savage, Pedersen, McCarthy, Roberts. Subs: Mokoena (Tugay, 46), Derbyshire (Bentley, 65), Rigters (McCarthy, 65). Subs not used: Dunn, Henchoz, Berner, Brown
The second leg take's place at Ewood Park on Saturday 28th July.