Kyle Lafferty grabbed the only goal of the game as Rangers moved nine points clear at the summit of the Clydesdale Bank Premier League.
The Northern Irishman netted in the second half after Steven Whittaker missed from the penalty spot just before half-time.
Rangers dominated the possession early on but both sides struggled to create much in the way of clear goalscoring opportunities in the opening spell. Gregg Wylde should have had the net bulging after 17 minutes when he raced on to a Steven Davis pass with only the goalkeeper to beat. Instead, Graham Stack made the save.
The youngster then squandered another great chance when Nikica Jelavic teed up the shot, Wylde blasting over when he should at least have tested Stack.
Wylde turned provider for Lafferty but he bulleted a header wide of the target, with the offside flag raised anyway. At the other end, goalkeeper Allan McGregor was called into action to block a well-struck effort from Ivan Sproule.
Stack then produced a great save to deny a point-blank shot from Jelavic after good play between the Croatian and Lafferty.
Rangers were handed a penalty on the stroke of half-time after Lafferty was brought down in the box by Stack after rounding the goalkeeper. But Whittaker blasted well over from the spot after winning the battle with Jelavic to step up for the pressure kick, as the first half ended goalless.
Hibs could have opened the scoring a couple of minutes after the interval when Paul Hanlon headed just over. The visitors had another great chance when Garry O'Connor released Junior Agogo into the box and the flag stayed down. McGregor blocked bravely at his feet, before Agogo smashed the rebound into the side netting.
The breakthrough finally came after 68 minutes when a Wylde cross into the box dropped for Lafferty at the back post and he fired home from six yards to hand Rangers the advantage.
The home side immediately set about trying to double their lead and Maurice Edu forced a decent save from the goalkeeper, before Jelavic followed up with the rebound that was offside. Stack then produced a superb one-handed save to prevent a ferocious strike from Davis finding the back of the net but Rangers managed to hold on for the narrow victory.
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