Former Hearts man Lee Wallace played a key role in the Rangers victory, scoring the opener just before half-time and then playing a part in a Kenny Miller strike which doubled the lead 10 minutes from time.
Runaway leaders Hearts will therefore be back in the Scottish Premiership next season while Stuart McCall claimed his first win as Rangers boss, in his third match in charge.
McCall’s men came into the match on a run of five straight draws, while Hibs were unbeaten since December and were looking for an eighth victory in a row.
But it was the visitors who were far more clinical and they are now back within three points of second-placed Hibs, with a game in hand also in their favour.
The first-half was a fairly disjointed affair, with clear cut chances thin on the ground.
Hibs defender Liam Fontaine did manage to get on the end of a Dylan McGeouch cross but he put his header wide of the target.
The hosts were having more of the possession but Rangers kept them fairly quite and went close themselves when Nicky Law curled a free-kick just over.
And the visitors took the lead a minute before half-time when Nicky Clark sent in a low cross, Miller flicked it on and, although defender Lewis Stevenson did well to foil Darren McGregor, the ball fell to Wallace, who swept it into the roof of the net from eight yards out, with the aid of a slight deflection.
The second-half was a lot more entertaining and Paul Hanlon headed just wide from a Hibs corner as the hosts attacked their task with a lot more vigour.
Hanlon then produced a brilliant piece of defending at the other end, sliding in to block a shot from Clark, who had been played in by Miller.
Hibs looked all set to equalise moments later when a slip from Bilel Mohsni set them up with a two-on-one situation but Marius Zaliukas managed to cut out Franck Dja Djedje’s square ball towards Dominique Malonga.
Scott Allan then had a shot from the edge of the area deflected wide as the hosts sought an equaliser in the final 20 minutes, only for Rangers to wrap up victory with 10 minutes to go, in hugely controversial fashion.
Wallace and Hanlon came together in the box and a couple of Hibs players appeared to stop, convinced that their player had been fouled.
However, referee Willie Collum thought otherwise and Miller took full advantage, latching onto the loose ball and scoring with a low shot from 16 yards out, as Rangers secured their most impressive success of the Scottish Championship season.