Moussa Diaby struck a brilliant goal to see off Rangers and earn Bayer Leverkusen a shot at Inter in the Europa League quarter-finals.
The French forward eased any Leverkusen nerves with his 51st-minute strike, securing a 1-0 win on the night and 4-1 aggregate success in the last-16 tie.
Kai Havertz had earlier gone close for the Bundesliga side, hitting the Rangers crossbar and sending another chance off target.
Rangers never looked capable of undoing the damage they sustained in the first leg, which was played at Ibrox in March, days before large parts of Europe went into lockdown.
It meant Steven Gerrard's side bowed out, but they at least produced a respectable performance at the BayArena, against opponents whose most recent game had been a DFB-Pokal final defeat to Bayern Munich.
Havertz, the 21-year-old attacking midfielder who may be in the final stages of his Leverkusen career, showed why the likes of Chelsea fancy him when a sublime attempt hit the Rangers crossbar early on.
He should then probably have done better after taking on a pass from Lars Bender but shot wide of the right post, but Havertz remained lively and fed Diaby for a sight of goal, only for the finish to go astray.
Diaby made amends for that miss in terrific fashion after the break, cushioning a pass delivered from halfway by Charles Aranguiz with his chest and burying a thumping finish high into Allan McGregor's net.
Leverkusen coasted from that point, preserving their energy for the clash with Serie A giants Inter on Monday in Dusseldorf, where a semi-final place will be at stake.