Joe Aribo gave Rangers the lead after 20 minutes with a fine drive after Ofir Marciano had scooped a Kemar Roofe header off the line. Rangers kept the pressure up and Nathan Patterson’s ball back into the danger area was knocked around by Roofe and Morelos before being hammered home by the Nigerian.
Rangers had already had the ball in the net by that stage though Roofe was flagged offside close in.
Hibs had their own chances at the other end and both Jackson Irvine and Kevin Nisbet fired drives wide of Allan McGregor’s goal and Paul Hanlon headed wide.
Aribo’s goal proved to be the only goal of the first but it was outdone in the second by an excellent finish from Ryan Kent – which the winger had threatened early on.
He took the ball away from Irvine and Alex Gogic before a drive found the inside of Marciano's netting.
Allan McGregor denied Gogic, Nisbet and Boyle in three top saves around the 70th minute mark and though the Scotland striker eventually headed past him, Rangers’ unbeaten run continues.
Match Verdict: Moira Gordon on Rangers 2, Hibs 1
Player ratings scale - 10: One of the best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: A terrible day at the office. 2: Abysmal. 1: One of the worst performances you've seen.
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9. Alfredo Morelos - 6
Striker was back defending and heading clear and often drifted off the front pairing with Roofe to link up play away from the box, but not a goal threat. Replaced by Hagi as Rangers switched attacking shape Photo: Ian MacNicol
10. Kemar Roofe - 8
Had ball in net ruled out for offside before a good header produced a stunning save from Marciano in lead-up to opener. Elegantly effective though and more comfortable central to an attacking trio. Photo: Rob Casey - SNS Group
11. Ryan Kent - 8
Looked sharp and positive from the start - fully benefitting from the recent break for internationals and Cove Cup game. Fired wide in the first half when taking initiative himself, then did likewise just after the hour for an excellent finish from range. Photo: Rob Casey - SNS Group
12. Steven Gerrard
Changed it up early on before reverting to tight midfield. Strong selection ensured all Rangers' options for Scottish Cup have had game-time in past fortnight. Photo: Rob Casey - SNS Group