The away fans felt they should have had a penalty as early as the fifth minute, but the contact between Chris Hogg and Steven Naismith appeared minimal and referee Steve Thomson waived play on.
The lively Merouane Zemmama was first to threaten for Hibs. His bursting run down the left took him past a couple of Rangers defenders, but as he wriggled his was into the box, a cut-back may have been a better option as he was crowded out by the Gers defence.
Barry Ferguson had the first great chance of the match in the 14th minute. Chris Burke's run and cross found Ferguson in space, but his left-foot effort was saved well by Yves Makaba-Makalamby, low to his left, but Scotland's skipper should have scored.
All the chances were falling to the league leaders and after he had earlier shot over, Lee McCulloch sent a header just past the post from a Charlie Adam cross.
Hibs then started to come more into the game and had a couple of chances in quick succession in the 40th minute.
As Zemmama's cross was headed down by Steven Fletcher to Dean Shiels, his weak shot was deflected wide off David Weir. From John Rankin's corner Fletcher stooped the head past Allan McGregor only to see his effort cleared off the line by Naismith.
Into the second half McCulloch had another headed effort, this time finding Makaba-Makalamby's gloves. That was followed by Rankin - on his home debut - having a good chance in the 49th minute, but he dragged his left-foot shot wide.
Tame efforts by Adam, McCulloch and Ferguson followed, then came a great effort by Hibs on 57 minutes.
A Brian Kerr knock-down from the corner of the box was volleyed at goal by Fletcher, but his exquisite drive was turned round the post by McGregor.
A minute later, Zemmama had time to lift his head and shoot but his 18-yard shot went straight at McGregor.
The next chance also fell to the home side on 62 minutes. Fletcher mis-controlled Zemmama's through ball, so forcing himself wide and as he rounded McGregor, Sasa Papac had got back to clear off the line.
Adam - the tormentor of Hibs from dead balls in the past - had a free-kick from 25 yards saved by Makaba-Makalamby on 67 minutes. This turned out to be Rangers' last real effort of the match.
Just three minutes from time there was drama as McGregor was shown a straight red card for hacking down Shiels as he ran through.
Neil Alexander came on for his Gers debut and saw Shiels' shot from the free-kick sail over, meaning a replay will now be required.