Dick Advocaat's side not only knocked out the last German side in the competition, they also gave notice that they can survive in this company and sent out a sombre message for any prospective opponent in today's draw.
With Colin Hendry leading by example, the defence was solid against increasing German attacks, providing a platform on which qualification was founded. Alongside the Scotland captain, Lorenzo Amoruso, Rangers' Italian captain who has been criticised in the past, produced one of his most commanding 90 minutes.
The 2-1 lead from the first leg ensured Rangers would not be too adventurous, but they always carried a threat through the explosive pace of Jonatan Johansson, Rod Wallace and Andrei Kanchelskis. Johansson, the flying Finn, made the breakthrough in the 56th minute, finishing a three-man surge into the German half with a powerful curling shot from 20 yards.
The Germans had created the best chances of the first half, notably for Erik Meijer, but the striker either finished wide or hit Lionel Charbonnier, the Rangers goalkeeper.
Rangers should have scored the second goal in the 77th minute, when Barry Ferguson, who had been valued at pounds 15m by Christoph Daum, the Germans' manager, before the first leg, found himself played through by Wallace, but he ran out of options and shot against the advancing goalkeeper.
Leverkusen brought themselves back into the game with 12 minutes remaining when Ulf Kirsten scored from close range, but they could do little thereafter to break down the Rangers defence.
Unfortunately for the Scottish side there was a downside even in victory as Charbonnier and later Ferguson were both forced to leave the field on a stretcher. The Rangers supporters, however, could savour the evening and a night of celebration before the draw, which will pair their side with one of Europe's top clubs and give Advocaat and his players another opportunity to extend the learning curve they have embarked upon so successfully this season.
Johansson appears stronger and more confident with every game, Kanchelskis has blistering pace and others, such as Arthur Numan and Giovanni van Bronckhorst, have settled in quickly. It is, however, the overall ability as a team that makes Rangers dangerous opponents.
Rangers (4-4-2): Charbonnier (Niemi, 66); Porrini, Hendry, Amoruso, Numan; Kanchelskis (I Ferguson, 66), B Ferguson (Wilson, 90), Van Bronckhorst, Albertz; Wallace, Johansson. Substitutes not used: Amato, Petric, Vidmar, Miller.
Bayer Leverkusen (4-4-2): Matysek; R Kovac (Emerson, 38), Nowotny, Happe, Heintze (Reichenberger, 65); Reeb, Ramelow, Beinlich, Ze Roberto; Meijer (N Kovac, 76), Kirsten. Substitutes not used: Zivkovic, Rink, Mamic, Vollborn (gk).
Referee: L Batista (Portugal).