Steven Davis opened the scoring in the first half with a tidy finish before his countryman David Healy took advantage of poor defensive play to add a second on 55 minutes.
This led to the club’s new signing Mervan Celik getting a run-out before man-of-the-match Sone Aluko added a third with a fantastic free-kick after James McPake had been shown a red card for a second bookable offence.
Davis then netted a fourth in injury time to cap an excellent display from the skipper.
With Nikica Jelavic out due to illness and Hibs’ top scorers Garry O’Connor and Leigh Griffiths both suspended Ally McCoist and Pat Fenlon had to shuffle their packs prior to kick off.
Aluko joined Healy in attack for the champions and the skilful Nigerian could have scored after just four minutes when Hibs failed to deal with a corner and his netbound effort from eight yards hit his strike partner in the back.
But with 12 minutes on the clock it was Eoin Doyle that was guilty of squandering a guilt-edged opportunity for the visitors.
The former Sligo Rovers striker found space behind the Gers backline but having received the ball he hesitated and allowed Bartley to sprint back and make a crucial block.
As expected Fenlon’s men worked hard with Sproule a threat in the early stages but on 26 minutes the opening goal arrived from Davis and it was a well worked move.
With Hibs committing men forward Edu played in Aluko and his flick was perfect for Davis who advanced in on goal and slotted it low past Brown.
On the half hour mark Edu came close to doubling his side’s advantage when he let fly from 20 yards but the ball flew inches wide of the post.
Aluko then produced a few trademark twists and turns to get away from his marker but his right foot curler from distance went straight into Brown’s arms.
Into the second-half and Rangers continued their search for a second goal and it arrived on 55 minutes thanks, in part, to a defensive mix up.
A long ball bounced through to Brown who tried to head the ball away but it landed at Healy’s feet and he produced a composed finish on the spin for his third goal of the season.
Rangers were now in cruise control and with Celik on in place of Wylde the third goal arrived and it was an absolute cracker.
McPake saw red for a poor tackle on Edu and, to make matters worse for Fenlon and his players, Aluko stepped up and curled a left foot shot over the wall and into the top corner of Brown’s net.
This looked to be the end of the scoring but with second remaining Davis again popped up in an advanced position and his shot across the keeper clipped the post before going in.
The result means that Rangers are now off league leaders Celtic, who are in Scottish Cup action tomorrow, while Hibs’ struggles this season continue.