A first-half goal from skipper Lee McCulloch proved to be the difference between the two sides in Germany in a match where the visitors had a few decent chances.
The outing also provided new signing Arnold Peralta with his first Rangers appearance after the Honduran was thrown into the action in the second half.
Hearts managed to put their off-field troubles to one side to claim an emphatic 5-0 victory over Raith Rovers at Starks Park - their second pre-season win.
Kevin McHattie, Billy King, Jamie Walker, Ryan Stevenson and Gary Oliver all helped themselves to a goal apiece for the Jambos.
The Edinburgh side had also defeated fellow administration-hit outfit Dunfermline at the weekend.
Inverness secured a comfortable 4-0 win over Highland rivals Clachnacuddin.
The match remained deadlocked at the interval but a double from Calum Ferguson and goals from Ryan Christie and Jason Brown in the second half saw Caley Thistle run out 4-0 winners.
The clash between Kilmarnock and East Fife was a closer affair, with trialist Ryan Harper grabbing the only goal of the game at Bayview.