Danny Röhl’s side fell behind just moments into the contest when Martin Boyle cracked open proceedings inside just four minutes when he volleyed beyond Jack Butland.
Thelo Aasgaard levelled proceedings with a quite sumptuous free-kick later in the first-half, but it was Hibernian who claimed all three points against the run of play when Dane Scarlett tapped home the winner with just two minutes remaining of normal time.
Before the match departing Hall of Fame captain, James Tavernier, was presented with an award for his incredible service over the last 11 years at the club by the Greatest Ever Ranger and a close confidant, John Greig.
Ibrox was grateful in its appreciation for the Englishman who arrived as a fresh-faced 23-year-old in the summer of 2015 and went on to win everything on offer domestically, captain the club to a UEFA Europa League final, and post individual goal contributions previously unheard of for a player in his position.
The action began with an opportunity of the clear-cut variety when an inswinging delivery from Connor Barron was met by Emmanuel Fernandez unmarked from close-range, but the defender could only power his header straight down the throat of Raphael Sallinger.
Rangers were made to pay just two minutes later when Hibs broke the deadlock through a familiar name. Jordan Obita was the architect down the left-hand side when he was afforded the time and space to deliver towards the back post where Boyle lurked to volley through the legs of Jack Butland.
In truth, the goal arrived against the run of play as the Gers continued to surge forward in the minutes after.
Mikey Moore danced through a succession of Hibs bodies on the edge of the penalty area, his initial effort blocked before it fell to Thelo Aasgaard in a promising area but the Norwegian international shot straight into the vicinity of Sallinger.
The on-loan Spurs wide man turned provider moments later as Dujon Sterling volleyed over, while Youssef Chermiti latched onto a lofted pass from Barron before being denied from a tight angle by the Hibs goalkeeper.
Indeed, Sallinger appeared on a one-man mission to repel everything that Rangers had to offer as Barron let fly with a terrific long-range half-volley which looked destined for the postage stamp before the goalkeeper’s full-stretch intervention.
He wasn’t required when Aasgaard did tremendously well to fashion a half-yard on the edge of the penalty area and the midfielder, one of two changes from Sunday, curled wide of the target.
But it mattered little as the summer arrival hauled the Gers back on level terms in quite emphatic fashion.
After winning the initial free-kick right on the edge of the penalty area following neat interplay through the heart of the visitors, he set his sights on the far top corner and whipped a thunderous curling effort which sailed into the top corner.
There was no doubt that the home side were the superior of the two teams in the contest, and the second period began in much the same way as Tuur Rommens attacked menacingly down the left before watching his low delivery hacked clear by Jack Iredale.
Chermiti threatened minutes later when Oliver Antman laid back into the Portuguese’s path, but it was always going to take something special from the forward to beat Sallinger from the distance and angle in which he was positioned.
Danny Röhl turned to his substitutes bench for inspiration just beyond the hour mark when Bojan Miovski, on the scoresheet against the Edinburgh outfit in the Premier Sports Cup earlier this season, joined the forward line.
He ought to have completed the turnaround for the hosts just minutes later when a dangerous move down the left-hand side saw Rommens pick out Moore inside the penalty area.
The teenager swept goalwards first-time on his unfavoured left side and was denied by the outstretched Sallinger, but when the ball broke kindly for the North Macedonian he contrived to stab the rebound over the top from a central position.
The sting had been taken out of the contest somewhat as the contest ticked into the final quarter of an hour.
Djeidi Gassama and Tochi Chukwuani were summoned from the bench in search of a winner, with Miovski causing a brief moment of panic inside the Hibs penalty area when he met a Jayden Meghoma delivery and forced Grant Hanley into a desperate block.
Down the opposite end, the Gers were almost the architects of their own downfall when a swift counter-attack sent Dane Scarlett through.
The substitute was denied initially by Butland at his near post, before the Rangers No.1 sprung quickly to deny Felix Passlack who looked to curl home on the rebound from the right-hand side of the danger area.
And Hibs found the winning goal with just two minutes remaining on the referee's stopwatch when Rangers failed to deal with an attack down Hibs' right-hand side.
Passlack hit the byline before squaring the ball across the six-yard box for Scarlett to provide the finishing touch on the goalline.
RANGERS: Butland, Sterling (Meghoma, 79), Fernandez, Djiga, Rommens (Aarons, 71), Barron, Diomande (Gassama, 71), Aasgaard (Chukwuani, 79), Antman (Miovski, 62), Moore, Chermiti
Subs not used: Kelly, McGuire, Souttar, Skov Olsen
HIBERNIAN: Sallinger, Hanley, O’Hora, Boyle (Scarlett, 77), Chaiwa, Iredale, Obita (N. Cadden, 77), Barlaser (Newell, 45), Passlack, Campbell (Mulligan, 67), Elding (Suto, 67)
Subs not used: Smith, C. Cadden, Andrews, Bushiri