Mikey Johnston, Odsonne Edouard and Scott Sinclair got the goals in Bosnia as Neil Lennon's team took command of the tie.
Rangers also enjoyed an emphatic away win, defeating St Joseph's 4-0 in Gibraltar in their Europa League qualifier. All the goals came in the second half, with Ryan Jack, Sheyi Ojo, Borna Barisic and Alfredo Morelos on target for Steven Gerrard’s men.