Sam Stanton gave Hibs an early lead before Rangers, in their first competitive match under new boss Mark Warburton, struck three goals in nine minutes through James Tavernier and a Martyn Waghorn double.
Andy Halliday and Kenny Miller, with a brace, added further strikes after Jason Cummings had briefly given Hibs hope from the penalty spot.
The home side squandered a great opportunity in the fourth minute when Cummings arrived at the back post to meet a clipped delivery from Paul Hanlon, but sent his header against a Rangers defender.
Five minutes later Rangers struggled to clear their lines at a Hibs corner and David Craig picked out Lewis Stevenson with an angled cross and he laid the ball back for Dominique Malonga, but the striker smashed his shot high over the target from 15 yards.
But Hibs finally made the breakthrough in the 14th minute when Stanton picked the ball up just inside the Rangers half and ran at the heart of the defence before dispatching a low shot from 25 yards into the far corner.
The visitors threatened on 21 minutes when David Templeton slipped a pass in front of Lee Wallace running into the penalty area and the ball broke in front of Jason Holt who stabbed wide under pressure from a Hibs defender.
With the game approaching the half-hour mark Hibernian missed a glorious chance to double their advantage when Stanton delivered a free-kick from the right flank and Liam Fontaine nodded the ball wide from six yards with the goal at his mercy.
Hibs had been dominant so far, but it proved to be a costly miss as the match was turned around late in the first half.
Hanlon brought down Holt right on the edge of the box and, from the resulting free-kick, Rangers full-back Tavernier (39) curled the ball into Mark Oxley’s top right corner.
Five minutes later Tavernier combined with Holt at the edge of the Hibernian penalty area and the midfielder’s low cross was bundled over the line by the unmarked Waghorn.
Waghorn added his second two minutes after the break when he latched on to a punted clearance from Rob Kiernan and crashed a shot under Oxley from the left side of the penalty area.
Cummings gave Hibs a lifeline on the hour, shortly after Rangers target Scott Allan had come on as a substitute for the hosts, when he sent Rangers ‘keeper Wes Foderingham the wrong way with a composed spot-kick moments after Halliday tripped him.
Halliday atoned for that error two minutes later when he stepped on to a cut-back from the right flank and chipped Oxley from 20 yards, with the ball bouncing over the line off the underside of the bar.
Miller arrived to clip a driven cross from fellow substitute Nicholas Clarke over the line with 13 minutes remaining, and the striker tucked another delivery into the roof of the net five minutes later.