The visitors got off to the perfect start, going a goal up in only the second minute. Chris Hogg did not get enough on a headed clearance inside the area, the ball dropping to ex-Hibs man Steven Whittaker 25 yards out and he unleashed a fine dipping left-foot shot that went over Grzegorz Szamotulski and into the net.
Hibs were almost level in the ninth minute, some intricate passing around the Rangers area lead to Derek Riordan finding some space, but his volley flashed wide with Neil Alexander stranded.
After his goal Whittaker was also the hero at the other end, coming in with a last ditch tackle on Colin Nish, who had been fed well by Steven Fletcher on 15 minutes.
Ten minutes later Maurice Edu had a chance at the back post, but could not get enough on a Steven Smith free-kick.
Andreas Velicka was next to threaten, but some tight Hibs marking meant he could not get a decent shot away from close range.
That was to prove costly as Hibs went up the other end and equalised in 34 minutes. Lewis Stevenson got free on the left to float a ball into the box, which was met by a glancing header by Fletcher and Alexander could only watch as it found the corner of the net.
By now Hibs were the better side, and substitute Jonatan Johansson forced the first save of the match out of Alexander, who had to dive low to stop the Finn's shot creeping in.
The second half started as openly as the first, and once more the Glasgow side got an early goal. Ex-Hearts man Velicka, who was about to be substituted, found space in the box and drove a fierce shot from an angle past Szamotulski at his near post.
Kris Boyd, who had been very quiet all afternoon, could have killed the game off just before the hour mark. Another Smith free-kick caused problems in the Hibs box, but Boyd missed his kick in front of goal when any touch would have found the net.
In a similar fashion to Velicka's goal, Riordan almost brought the home side level in 70 minutes, but Alexander was able to beat away his shot for a corner.
The fresh legs of Kenny Miller almost a third for Rangers, but Szamotulski turned his shot wide after Miller had skinned Hogg.
From the resulting corner the visitors did get their third goal. A scramble in the Hibs box saw Sol Bamba do well to clear one net-bound effort, but Edu was following up to blast high into the Hibs' net on 73 minutes.
Not long after that and Miller once again got the better of Hogg and got a shot away from a tight angle, but Szamotulski deflected it wide.
John Rankin then set up a grandstand finish, with a left-foot bullet from 25 yards which flew into the top corner with five minutes to go, but an equaliser did not come.