Eventually it was the top-scorer Kris Boyd who broke the deadlock just after the hour-mark with a superb finish.
This victory sets up the home team nicely for their Old Firm encounter next Saturday against Celtic.
Rangers should have taken an early lead when Pedro Mendes' through ball found Boyd beating the offside trap, but the striker's shot was blocked by keeper Yves Makaba-Makalamby.
From a Steven Davis corner, Kirk Broadfoot's header was straight at the keeper who gathered easily.
Rangers dominated the early proceedings with Mendes and Barry Ferguson controlling the midfield.
A long-range shot by Mendes had Makalamby scrambling along his line to save.
Kenny Miller volleyed over from Kyle Lafferty's cross before Steven Whittaker bent a marvellous cross behind the defence but there were no takers as the Rangers attack was caught flat-footed.
Hibs wasted a great chance just before the interval when a long clearance found Colin Nish clear inside the centre circle but, rather than advance on Allan McGregor, he tried to chip the keeper but his effort was hopelessly wide.
The home support were becoming increasingly frustrated with Rangers' inability to break down the Hibs defence and early in the second half Chris Hogg produced a marvellous tackle to deny Miller.
Just when Rangers looked to have run out of ideas they opened the scoring.
A deep corner by Davies was headed on by Broadfoot and with his back to goal Boyd's overhead shot found the far corner of the net.
For the first time, Hibs started to threaten Rangers and John Rankin's long-range shot dipped just over.
Then Steven Fletcher should have done better with his header when Alan O'Brien's cross found him in space six yards from goal.
Mendes nearly added to Rangers' lead with ten minutes remaining but his audacious chip from fully 35 yards came back off the face of the bar.