The Glasgow side started brightly, and only alert defending by Ian Murray denied Charlie Adam a great chance in the opening two minutes. Hibs were not finding the target with their passes, and this nearly led to Rangers opening the scoring.
Chris Hogg gave the ball away under no pressure and Kenny Miller should have done better than dragging his shot wide from the resulting opportunity.
Despite the visitors bossing the play, it was Hibs that had the first real effort on goal in the 15th minute. Returning hero Derek Riordan slipped in Dean Shiels, but his powerful effort was straight at Neil Alexander who palmed the ball away for a corner.
Just as Hibs were beginning to come into the game they were hit with a sucker-punch in the 31st minute. Souleymane Bamba had just seen his header cleared off the line when Rangers broke up the field for the opener.
The ball found its way to Kirk Broadfoot on the right, and his low cross was met by Miller's diving header, which went across the keeper and into the far corner of the net.
Hibs did not let their heads go down and were almost level five minutes later. Riordan got to a lost ball and hit a superb cross which was volleyed onto the post by Murray, before Sasa Papac and Alexander completed the clearance.
Hibs are a side that have had defensive troubles all season, and that trend continued. Just before the interval Pedro Mendes and Broadfoot combined to set up Miller to make it 2-0, with the home defence nowhere.
Miller's curled left-foot finish was a fine one, but he should never have been left in so much space.
In the second half Hibs never looked like coming back into it. Joe Keenan had a shot comfortably saved by Alexander ten minutes in, but did nothing else of note.
More poor defending by Hibs left Jean-Claude Darcheville with a clear path to goal but he could not capitalise on his 58th-minute chance.
Rangers made the game safe with 17 minutes to go, as they punished Hibs for falling asleep at the dead ball. Ex-Hibs man Kevin Thomson delivered the ball in, and Madjid Bougherra had the simplest of tap-ins at the near post, his first goal for the Gers.
Miller had a chance to grab a hat-trick with five minutes to go, but his driven effort from the right flew wide. Minutes later Kyle Lafferty and Nacho Novo went close, but Rangers had to make do with 3-0.