Daizen Maeda scored the decisive spot-kick for the Bhoys, while Ridvan Yilmaz missed his opportunity as Celtic ran out 5-4 penalty shoot-out winners at Hampden Park on Sunday.
The match ended 3-3 after extra time. The Gers took the lead through Nadim Baramin after pouncing on a mistake made by Greg Taylor.
The left-back made amends when he scored the equaliser, although the shot took a deflection on the way. Maeda made full use of a defensive mistake to make it 2-1 for Celtic, but Rangers restored parity 15 minutes later through Mohamed Diomande.
When Nicolas Kuhn scored in the 87th minute, it felt like he had netted the winner, but Danilo brought Rangers back into the game again when he scored from a header shortly afterwards to take the match to extra time and then to a penalty shoot-out.