The visitors travelled to Glasgow in the bottom two on Monday night and without a point on the road this season, but Jason Cummings’ double and a David Gray goal put them 3-0 ahead at half-time as the home crowd vented their anger.
Nicky Law’s reply did lead to Rangers pressure after the break, but Hibs held out to move up to fifth and leave their hosts still six points off leaders Hearts.
An open game got its first goal after 25 minutes as Arnold Peralta’s failure to deal with Mark Oxley’s punt allowed Cummings in for a shot which Steve Simonsen reached but could not keep out.
Gray headed in Lewis Stevenson’s cross (31) before Ian Black lost possession to spark a Hibs counter which Cummings finished off for his fourth goal in five games.
Ally McCoist removed Peralta at half-time and saw Law volley in (55) before Black’s free-kick was kept out and Kris Boyd had a goal ruled out for offside.
But Hibs had chances on the counter and saw the game out to avenge August’s League Cup defeat.