A first half full of attacking endeavour from the Light Blues was rewarded as Bailey Rice converted from the penalty spot following a foul on Cameron Cooper.
The home side then extended their advantage through Findlay Curtis midway through the second half to cap off a controlled performance and seal their place in the next round.
Cameron Campbell named two changes to his side for the visit of the Hibees, with Zak Lovelace and Greig Allen replacing Tyler Pasnik and Kieron Willox from the team which played out a 3-3 draw with Hearts last time out.
The Gers seen plenty of the ball in the opening exchanges without too much goalmouth action, with Kristian Webster sending a couple of searching diagonals to pick out Zak McKay on the opposite flank.
McKay himself sent a speculative effort over the crossbar on ten minutes, before the Gers were awarded the opportunity to break the deadlock from the penalty spot five minutes later.
Kerr Robertson lifted his head in midfield and picked out a lovely pass towards Cameron Cooper who was darting in-behind the Hibs defence. The Gers No.10 controlled the ball at the corner of the penalty area before his heels were clipped by Ricky Waugh as the pair crossed paths. Bailey Rice stepped up to take and dispatched confidently, sending the goalkeeper the wrong way to give Rangers the lead.
The Light Blues were buoyed by the goal and they almost doubled their advantage four minutes later as Cooper connected cleanly with a rasping strike and drew a fantastic diving stop from Freddie Owens in the Hibs goal.
Webster then met the resulting corner at the far post, climbing the highest from an inswinging delivery, with his downward header bouncing dangerously around the six-yard box before it was eventually cleared to safety by the visitors.
Rangers had certainly found their groove, with Cooper and Curtis dovetailing to good effect on the right-hand side of the penalty area before the Hibs defence intervened as the latter shaped to the shoot.
A well-worked move from the hosts on 26 minutes almost engineered a terrific second goal. McKay received a pinpoint diagonal from Webster on the left touchline before laying the ball back to Rice for a crossing opportunity. The goalscorer sent a dangerous curling delivery into the penalty area which was met by Curtis but his header was saved by Owens.
Rice tested the Hibs goal with a curling free-kick from a central position on 37 minutes, forcing Owens into a diving stop to his right to tip the ball around for a corner.
The Gers emerged with a renewed intent for the second half, with Rice going close from another set-piece before Curtis was flagged offside after Robertson picked the attacker out with a deft floated pass.
Lovelace had a sighting of goal to stretch the Gers’ advantage in the 56th minute, racing onto Cooper’s through pass before drilling a low effort that the goalkeeper was equal to.
The away side fashioned an effort at goal themselves on 63 minutes as Ethan Laidlaw curled wide of Jacob Pazikas’ goal.
The second goal for the Gers on the evening arrived just shy of the 70th minute mark. Lovelace did well to race away from his marker on the left, speeding to the byline before picking out Curtis haring into the penalty area in the middle. The attacker opened up his body and stroked a side-footed first-time finish under the body of the Hibs goalkeeper to double his side’s advantage.
Cooper and Lovelace linked up to good effect once again just minutes later, with Owen Hastie producing an expert sliding challenge to block the latter’s effort at goal.
A third goal for the Gers almost arrived 13 minutes from time. Cooper turned in space in the centre of the pitch before unleashing at goal, with his effort inches away from landing in the top corner.
Substitute Jack Wylie tested his luck from range on 86 minutes, stepping effectively into midfield and eyeing up a speculative effort that travelled off target.
The referee blew the full time whistle to confirm the Light Blues’ pace in the next round of the Scottish Youth Cup, with attention now shifting back to league action for Campbell’s side.
RANGERS U18s: Pazikas, Webster, Allen (Wylie, 63), Grant, Hutton, Rice (Mulindwa, 80), Robertson, McKay (Scott, 80), Curtis (Willox, 72), Cooper, Lovelace
Subs not used: Kane, Rogerson, Eadie
HIBERNIAN U18s: Owens, Geaney, Waugh (McGarva, 64), Khan, Hastie, MacIntyre, Landers (Smith, 80), McCallister, Laidlaw, Molotnikov, Holden (Whittaker, 45)
Subs not used: McLean, Gardner, Craig, Samuels