This was surely a night when Manager Walter Smith got his team selection and tactics wrong - illustrated by his making two changes at the interval following a dreadfully disappointing first-half.
The Ibrox Boss made one change from Saturday with Andrius Velicka replacing the injured Kenny Miller at a venue where Rangers have already chalked up two wins this season.
It took the game some time to get going - Kris Boyd having the first goal attempt in sixteen minutes when his shot from a Pedro Mendes interception was deflected wide.
Four minutes later Mendes himself saw his twenty-yard shot from a Steven Whittaker pass flash just wide of the target.
An uninspiring first-half looked to be drifting towards the interval goalless when Hibs took the lead in forty minutes with a spectacular Derek Riordan goal when he curled the ball home from the edge of the penalty area from a Steven Fletcher lay-off.
Rangers had lacked pace and penetration up front - and Walter Smith sought to rectify that by introducing both Nacho Novo and Kyle Lafferty in place of Steven Smith and Velicka. In truth, at least another two could easily have found themselves substituted.
The visitors were transformed after the break - with Novo's speed and enthusiasm the key along with Lafferty's skill and mobility.
The first moment of controversy arrived in 49 minutes when Boyd's header from a Novo cross was held by Yves Ma-Kalambay - but it did look as if the home goalkeeper had carried the ball over the line as he turned. That however was nothing to what would follow...
Novo could have had a double inside the next three minutes as firstly he skied Lafferty's cross over the bar with the goal at his mercy - then in the very next attack he sliced the ball wide after a surging run by Steven Whittaker had taken him to the bye-line, his cutback begging to be converted.
Lafferty was next to spurn a golden opportunity in 55 minutes when he shot wide from a Steve Davis cross - and the two Ulstermen combined again on the hour when Davis' twenty-yard shot from Lafferty's lay-off was turned wide by Ma-Kalambay.
Rangers were laying siege to the home goal - but were vulnerable to the counter-attack, as was illustrated in 65 minutes when Riordan cut in from the right before seeing his 25-yard shot held by Neil Alexander.
The game exploded in controversy three minutes later when from a Pedro Mendes corner Boyd's header was blocked, Novo seizing the rebound to prod the ball over the line before it was hooked away by Ross Chisholm. It was a goal - and that appeared to confirmed by linesman Martin Cryans who started to run towards the halfway line only to stop when he realised that Referee Eddie Smith had hesitated in making a decision.
The linesman was surrounded by protesting Rangers players - to no avail - and the feeling of injustice was compounded when both Mendes and Lafferty were yellow-carded for dissent.
The Ibrox men had been cheated - and were again in 72 minutes when Novo was sandwiched between Chris Hogg and Rob Jones. To no-one's surprise however Eddie Smith waved play on - this is a referee after all who in his everyday job as a police officer is based at London Road Police Station and regularly accompanies Celtic on European trips.
Two minutes later Riordan might have put the game beyond Rangers when he intercepted Madjid Bougherra's attempted clearance only to see his weak shot held by Alexander.
At last an equaliser arrived in 79 minutes when from a Bougherra cross an almighty scramble ensued in front of goal before Novo rammed the ball into the net.
Rangers piled on the pressure in the closing stages - and Novo should have done better in 87 minutes than direct a flying header from a Whittaker cross straight into the arms of Ma-Kalambay.
With time running out Novo cut in from the right before sending over a low driven cross that eluded both Lafferty and Boyd.
The final whistle signalled a serious blow to Ibrox title hopes - but also produced amazing scenes as many Hibs players effectively went on a lap of honour. What exactly were they celebrating?
Afterwards a disappointed Walter Smith reflected:
"I feel frustrated by the failure to win. We dominated territorially in the first-half without creating chances. The second-half was there for us - we missed several chances. We've already won here twice this season without dominating as we did tonight. We commanded the game from start to finish. We now have to beat Aberdeen on Saturday... "
The question remains however - why did it take Rangers 45 minutes to start playing?
HIBERNIAN Ma-Kalambay; Van Zanten, Hogg, Jones, Murray; Rankin, Bamba (Thicot 90), Chisholm, Stevenson; Fletcher (O'Brien 84), Riordan
UNUSED SUBS McNeil, Keenan, Hanlon, McCormack, Johansson
RANGERS Alexander; Dailly, Weir, Bougherra, Whittaker; Davis, Edu, Mendes, S. Smith (Novo 45); Boyd, Velicka (Lafferty 45)
UNUSED SUBS McGregor, McCulloch, Naismith, Fleck, Wilson
REFEREE Eddie Smith