The Glasgow side deservedly avenged October's 1-0 defeat to Hibs and temporarily overtook arch-rivals Celtic at the top of the table.
They have now gone seven league games unbeaten, but Hibs' statistics since winning at Ibrox - just one win in 11 games - says much about a team drained of confidence and desperate for a new manager following the shock departure of John Collins.
The signs had been ominous from the very start as Rangers settled quickly, while the hosts looked jittery and were unable to make their passes stick.
An already feverish atmosphere was fired up even further in the sixth minute when winger Chris Burke was sent sprawling inside the penalty area only for referee Charlie Richmond to wave play on.
But Burke would not be denied and, after Rangers skipper Barry Ferguson shot over from 20 yards, Burke hammered in a low cross from the right which was side-footed home by Steven Naismith from close range.
Hibs then enjoyed a decent ten minute spell without ever putting visiting keeper Allan McGregor under any pressure and Rangers soon began to turn the screw with striker Daniel Cousin twice testing keeper Yves Makaba-Makalambay.
The big keeper rescued his team five minutes before half-time when he blocked Ferguson's finish after the Scotland captain had weaved his way through the home defence.
Caretaker boss Tommy Craig brought on playmaker Guillaume Beuzelin and left winger Alan O'Brien for the second period and Hibs immediately looked more competitive with Dean Shields calling McGregor into action for the first time with a low angled shot before a sharp glancing header.
Rangers were undoubtedly wobbling, but the Ibrox ship was steadied in spectacular fashion as Burke kept calm in heavy traffic before picking out Cousin with a pass which he lashed left-footed high and into the top corner of the net.
Substitute Beuzelin wasted a free header which might have offered Hibs a lifeline and, even though Merouane Zemmama did pull one back near the end, Rangers could easily have added further goals themselves.
Defender David Weir tested Makaba-Makalambay from distance, while former Hibs skipper Kevin Thomson risked the fury of the home fans with a late free-kick which was deflected wide.