Both sets of youngsters produced an open and exciting affair with quickfire goal doubles for each side at the start of both halves.
However Young-Coombes’ 65th-minute header was decisive as Rangers lifted the trophy for the first time in five years.
Ibrox youth coach David McCallum said: “The character our players showed by going out and getting a winner after losing a two-goal lead is the biggest thing we can take from this. It was a really interesting final and we are delighted.
Rangers forced three early corners and, from the third, they took the lead when Kai Kennedy’s cross reached Ciaran Dickson at the edge of the box and he curled a shot past Liam Hughes
The lead was doubled a minute later when Dickson floated in a free-kick that Kyle McClelland headed away from goal. However it fell kindly for Scotland under-19 cap Adedapo Mebude to drill in from 18 yards.
It looked like Celtic’s evening was going from bad to worse when Chris McQueen was forced off with a nose injury and he was absent for over 10 minutes before re-appearing.
Being back to eleven players gave Celtic a boost and Dembele burst into life midway through the opening half when he exchanged passes with Scott Robertson before Lewis Budinauckas raced from his line to save.
Celtic’s Cameron Harper then let fly from 22 yards but Budinauckas dived to his left to save, with Barry Coffey also going close shortly afterwards.
Celtic made a substitution at the break with Dave McKay replacing Robertson and, incredibly, three minutes later, they were level.
Within 90 seconds, Dembele burst forward for 40 yards and released Harper who cut in from the left before sliding a shot into the corner. Celtic struck again before Rangers could draw breath with Paul Kennedy’s 30-yard free kick deflected off Mebude past Budinauckas.
Another set-piece was to prove decisive, with Kennedy crossing and Young-Coombes heading home from six yards.
Mebude was fouled by Brody Paterson in the box but Hughes’ penalty save prevented Kennedy from restoring Rangers’ two-goal lead.
Harper was denied a late headed equaliser due to the ball going out of play in the build up.
Celtic coach Stephen McManus said: “Everyone should have enjoyed that game. We asked the boys to show resilience and determination in the second half and they did that.”