With Fernando Ricksen and Peter Lovenkrands on top form on either flank, Lorenzo Amoruso solid at the back, Barry Ferguson in control in midfield and Tore Andre Flo back on the goal trail it was all too much for the Edinburgh men.
Flo scored twice while Lovenkrands claimed his first Tennent’s Scottish Cup goal and there was a great moment for Billy Dodds as he came off the bench with 20 minutes to go and scored his first goal in 13 months.
Hibs had some moments, especially when they levelled the game through Grant Brebner, but Rangers’ superiority told even although it was their fourth game in eight days.
Alex McLeish had demanded the same fire and passion Rangers had produced in the second half at Dunfermline on Wednesday and he got it as the Ibrox men made an explosive start to an engrossing Cup tie.
There was purpose and desire in everything they did and Hibs were lucky to remain intact in the early stages as Rangers swarmed at the Easter Road side.
As early as the second minute Shota Arveladze had a shot deflected for a corner. Fernando Ricksen whipped over the kick and Lorenzo Amoruso was denied when his header was diverted for another corner.
Peter Lovenkrands flashed a shot just wide two minutes later and then Nick Colgan did well to hold Tore Andre Flo’s header in six minutes as Hibs struggled to cope with the advances of the Light Blues.
There was no let up as Tony Vidmar won a freekick in 12 minutes after being fouled by Gary Smith but Amoruso’s effort was saved by Colgan. Then in 18 minutes Ronald de Boer was only a couple of inches too high with a terrific left shot after an excellent turn on the edge of the box.
A goal just had to come, such was Rangers’ intense pressure, and it was well worth the wait when it duly arrived in 22 minutes.
Amoruso started the move with a good ball wide to Ricksen, who had been effective on the right since the start of the match. The Dutchman picked out Arveladze with a low cross but the Georgian fooled Hibs with a brilliant dummy.
The ploy was perfect as the ball made its way directly into the path of Flo, who finished with deadly accuracy, sending a right foot shot into the right corner to claim his 20th goal of the season.
Frustratingly for the bench and the Ibrox crowd, Arveladze wasted an opportunity to virtually kill the game four minutes later when he was set free down the right by Amoruso.
With the Hibs defence on their heels, Shota simply had to measure his cutback as both de Boer and Flo were waiting in the middle but he hit his pass behind Flo and the chance was lost.
The significance of this was exemplified in the worst possible way just two minutes later when Hibs stunned the home crowd with an equaliser, scored by midfielder Grant Brebner.
No-one tracked Brebner as he burst into the Rangers box to collect a great pass from Ulises de la Cruz and he forced a terrific right foot shot which beat Stefan Klos.
In the end it only delayed the outcome but it meant that Rangers had to go and win the game all over again.
Craig Moore had a chance to repair the damage in 38 minutes when he was given a free header from Lovenkrands’ freekick after Townsley had fouled Ricksen but he tried to be too exact with his effort and flicked it wide.
However, young Dane Lovenkrands restored Rangers’ lead just before half-time and again it was a terrific move which produced the goal.
Bert Konterman played a good ball forward to de Boer, who had moved to the left side of the Hibs box and he cleverly eased away from Ian Murray before driving over a low cross which Lovenkrands swept into the net from six yards.
Flo may still have his critics, but his goals record speaks for itself and he made the game safe for Rangers with his second strike of the match 19 minutes into the second half.
This was much more opportunisitic in the sense that Ricksen’s corner was headed down by Amoruso and then knocked on by Vidmar, but Flo had the instinct to divert he ball into the net with his left foot.
Substitute Gary O’Connor did force Klos to make a decent save in 68 minutes after Vidmar had failed to clear his lines but that was about as close as Hibs got to forcing their way back into the game.
Rangers were comfortable and tormented Hibs in the final 20 minutes. They might have really hammered Hibs but in the end they only added one more to their tally.
That said it was a champagne moment for Billy Dodds. The striker, out in the cold under Dick Advocaat, came on for de Boer and scored his first Rangers goal in 13 months.
It came in 85 minutes when Vidmar found Dodds in the box with a crossfield ball. It looked as though he had missed his chance when he mis-hit his first shot but he regained his composure to fire a left foot shot into the net.
RANGERS: Klos; Moore, Konterman, Amoruso; Ricksen, Ferguson, Vidmar; de Boer (Dodds 70); Arveladze, Flo, Lovenkrands. Subs not used – Christiansen, Hughes, Ross, Caniggia.
Bookings: None
HIBS: Colgan; Murray, Smith, Fenwick, Lauresn; de la Cruz, Brebner, Jack, Townsley (Arpinon 68); Luna (O’Connor 45), Hurtado (Riordan 55). Subs not used – Caig, Dempsey.
Bookings: de la Cruz (83)
Ref: John Rowbotham.
Att: 25,636.
Man of the Match: Fernando Ricksen
Moment of the Match: Shota’s dummy to set up Flo for the first goal.