A breathtaking 44th-minute goal from Rod Wallace gave the Scottish champions a two-goal cushion to take to Dortmund in a fortnight for the second leg of this third-round tie, a far more assured position than they enjoyed on their previous trip to Germany earlier this month when Bayern Munich eliminated them from the Champions' League.
Dortmund were everything their recent bad press had promised. They deserved a D minus for becoming groundbreakers in Teutonic inefficiency and their wretched night was capped by Jurgen Kohler's own goal which set Rangers on their way. The current side are poor heirs to the one which won the European Cup in 1997.
However, to balance the scales, Rangers have had the core of a very settled side ripped out since their experience against Bayern Munich three weeks ago. Gone are Michael Mols, whose season ended with his knee injury that night, captain Lorenzo Amoruso through suspension, while the ex-Dortmund goalkeeper, Stefan Klos, could not face his old club because of a wrist injury which forced Rangers to recruit Thomas Myhre on loan from Everton.
It took an error, rather than a piece of inspiration, to break the deadlock. Gabriel Amato's low cross from the left was intended for Wallace but Kohler, the legendary German defender, tried to cut the ball out and only succeeded in diverting the ball past Jens Lehmann with his outstretched leg.
Dortmund's pride was stung and Fredi Bobic ought twice to have buried inviting crosses from Evanilson but failed miserably.
Rangers almost made the Germans pay for such profligacy in the 31st minute when Giovanni van Bronckhorst broke from his own half and released Wallace, but Lehmann was equal to the little striker's shot. Kohler tried to atone for his mistake five minutes later when he rose to meet Andreas Moller's free-kick, but Myhre clutched it confidently.
Rangers doubled their lead with a move of true quality seconds before half-time. Wallace started it, finding Van Bronckhorst who in turn fed Jorg Albertz. The German shaped as if to strike the ball, but craftily cut it back into the path of Wallace, who sweetly guided a right-foot shot beyond Lehmann.
Dortmund replaced Otto Addo with Giuseppe Reina in the second half, while Rangers' Jonatan Johansson came on for Amato, but amid the frenetic exchanges the game struggled to find any moments of true menace. Evanilson was booked on the hour although, perversely, Rangers were the more physical side.
Had substitute Neil McCann's header found the net, instead of the hoardings, the Bundesliga team could not have complained at the deficit.
Rangers (4-4-2): Myhre; Adamczuk, Moore, Vidmar, Numan; Reyna (Kanchelskis, 85), Ferguson, Van Bronckhorst, Albertz; Amato (Johansson, 44), Wallace (McCann, 67). Substitutes not used: Wilson, Nicholson, Durie, Brown (gk).
Borussia Dortmund (3-4-3): Lehmann; Worns, Feiersinger, Kohler; Evanilson, Stevic, Ricken (But, 72), Barbarez; Addo (Reina, h-t), Bobic (Herrlich, 83), Moller. Substitutes not used: De Beer (gk), Baumann, Nijhuis, Ikpeba.
Referee: U Meier (Switzerland).