Forget the narrowness of the scoreline - this was as comprehensive a 2-1 win as it is possible to imagine, as the home side were at times outplayed and outclassed.
Manager Walter Smith made one change from Boxing Day with Brahim Hemdani replacing the injured Charlie Adam.
Rangers were on top from the opening seconds - and had a strong appeal for a penalty turned down in five minutes when Chris Burke was knocked off the ball by Lewis Stevenson as he homed in on a Kevin Thomson pass. Referee Charlie Richmond waved play on however.
Six minutes later the visitors took the lead when Alan Hutton's throw-in found Burke whose low driven cross was smashed into the roof of the net from close range by Steven Naismith.
The Ibrox men were in control - and might have added a second on the half-hour mark when home goalkeeper Yves Ma-Kalambay fumbled a Thomson free-kick but recovered in time to block David Weir's effort from the rebound.
Two minutes later Daniel Cousin's 25-yard shot cannoned back off Ma-Kalambay's chest.
It was all Rangers - a sweeping Burke - Naismith move in 34 minutes released Cousin whose shot was blocked by the Hibs goalkeeper.
Six minutes later Naismith released Barry Ferguson whose drive was blocked by the Belgian goalkeeper.
Somehow the interval arrived with Rangers only one goal to the good, when it really should have been at least three.
The Leith side had been so far out of things that Head Coach Tommy Craig made a double substitution at the interval with Alan O'Brien and Guillaume Beuzelin replacing Filipe Morais and Patrick Noubissie.
Hibs did make a positive restart - Dean Shiels shot from O'Brien's cross in fifty minutes being the home side's first effort on target. Allan McGregor was equal to the task on that occasion, as he was again five minutes later when he again denied Shiels, this time a header from Thierry Gatheussi's cross.
Rangers soon underlined their superiority however when Cousin rifled home a Burke pass from the edge of the box in 58 minutes.
Six minutes later Burke's corner broke to David Weir whose twenty-yard drive was touched over by Ma-Kalambay.
Jean-Claude Darcheville made a welcome return in 74 minutes when he replaced Cousin.
Rangers were now in absolute control, keeping possession almost at will as the Easter Road men were totally humiliated.
The home fans were pouring out of the ground long before the final whistle - with the 'Famous Five Stand' in particular emptying at a rapid rate.
Unbelievably despite the Light Blues total supremacy it was Hibs who put a totally unrealistic slant on the scoreline in 87 minutes when Merouane Zemmama netted with a twenty-yard shot after Lewis Stevenson's cross was nodded down to him by Brian Kerr.
That proved no more than a consolation however - and afterwards a relaxed Walter Smith summarised:
"I'm delighted with the win. We had lots of possession in the second-half, perhaps too much, and that led to slackness late on and a nervy last few minutes. Easter Road is a very difficult place to come."
Hibernian Head Coach Tommy Craig was honest enough to admit:
"It was a torrid second-half. Rangers were by far the better team. This may be a big step forward for them."
HIBERNIAN Ma-Kalambay; Gatheussi, Hogg, Jones, Stevenson; Morais (O'Brien 45), Kerr, Noubissie (Beuzelin 45), Chisholm; Shiels, Donaldson (Zemmama 62) UNUSED SUBS Grof, McCormack, Antoine-Curier, Lynch
RANGERS McGregor; Hutton, Cuellar, Weir, Whittaker; Burke, Ferguson, Hemdani, Thomson, Naismith; Cousin (Darcheville 74) UNUSED SUBS Carroll, Ehiogu, Broadfoot, Boyd, Furman, Efrem
REFEREE Charlie Richmond