The Easter Road side headed into the clash joint-bottom of the table and with few backing them to cause an upset but they stunned their hosts thanks to goals from Liam Miller, John Rankin and Francis Dickoh.
The victory took Hibs to eighth in the SPL, while Rangers were able to retain their single-point advantage at the summit after Celtic also suffered defeat at Hearts.
Rangers made one change from the side who defeated St Mirren at the weekend. Kyle Lafferty was rewarded for his efforts on Sunday with a starting role, while Vladimir Weiss had to settle for a place on the bench as he recovers from a troublesome heel problem.
Hibs made four changes from the side who lost the Edinburgh derby to Hearts. Ian Murray, Dickoh, Valdas Trakys and David Wotherspoon all started, with Derek Riordan suspended and Lewis Stevenson, Paul Hanlon and Danny Galbraith dropping to the bench.
Hibs goalkeeper Mark Brown was called into action after just a couple of minutes to tip a rasping shot from Steven Naismith over the crossbar following an early period of pressure from Rangers.
But it was the visitors who surged into the lead after six minutes thanks to an ambitious 30-yard strike from Miller. Allan McGregor initially appeared to have the shot covered but a slight deflection took the effort past the Rangers goalkeeper.
McGregor was then called upon to produce a terrific save at point-blank range to prevent a Wotherspoon shot from finding the back of the net.
His heroics were matched by Brown at the other end when Steven Whittaker released Madjid Bougherra and he slipped into the path of Lafferty, who was denied the leveller as the Hibs goalkeeper blocked with his foot.
Rangers were stunned when Hibs doubled their lead after 19 minutes. Rankin exchanged a one-two with Trakys before rifling a right-foot shot past McGregor from 25 yards.
Only some last-gasp defending from Hibs prevented Rangers from pulling a goal back when David Weir met a Steven Davis corner with a firm header that appeared netbound only to be nodded off the line and onto the post by the alert Trakys.
The visitors demonstrated their stubborness again when a corner broke for Bougherra and he tried his luck with a ferocious effort that was also blocked on the line, this time by Michael Hart.
There was a further set-back for Rangers when Maurice Edu left the action on a stretcher a couple of minutes before half-time and was replaced by Weiss. Sasa Papac was then carried off as well, following a clash of heads with Wotherspoon, with Kirk Broadfoot thrown into the action in injury-time.
Rangers emerged for the second half determined to haul themselves back into the game and Weiss teed up the shot in front of goal for Lee McCulloch but Brown came to the rescue again for Hibs.
McCulloch then won a foul 35 yards out following a challenge from Dickoh but Weiss was just a bit too ambitious with a looping long-ranger that was comfortably smothered by the Hibs goalkeeper.
Rangers continued to push forward and Whittaker supplied a lovely long ball for Kenny Miller who immediately bore down on goal in search of his 15th goal of the season but Sol Bamba snatched the ball from his foot before the striker could even unleash the shot.
Hibs knew another goal would snuff out any chance of a Rangers comeback and Rankin was not too far away with an opportune strike from distance that a full-stretch McGregor only just managed to tip over.
But the goalkeeper was picking the ball out of the back of the net again with 76 minutes gone as the Edinburgh side made the most of the resultant corner.
Rankin swung the ball into the packed goalmouth where Bamba was waiting to nod on for Dickoh and he left McGregor with no chance of stopping his volley from hitting the target and securing a much-needed win for Hibs.