Philippe Clement’s side were rampant from the get-go, breaking the deadlock inside six minutes through Ianis Hagi before Robin Propper doubled the side’s lead midway through the second period.
Danilo then sprung from the substitutes bench to put the ribbon on a thoroughly dominant display from the Light Blues.
The Gers began with a makeshift backline owing to the injury-enforced absences of captain James Tavernier and Jack Butland, with the manager turning to Liam Kelly and Ridvan, operating on his unfavoured side, to fill the considerable void.
Indeed, the duo were two of six changes from the side who were held at Fir Park on Sunday; Jefte, Ianis Hagi, Vaclav Cerny and Nedim Bajrami also in from the off.
January 2nd is always a poignant day in the Rangers calendar and both sides paid tribute to the victims of the Ibrox Disaster before kick-off.
Rangers set out an early marker inside four minutes when a dangerous delivery was headed only as far as Bajrami by Cameron Carter-Vickers, although the Albanian’s volley was blocked from close-range and the subsequent melee led to a desperate Celtic clearance.
And with only six minutes on the clock it was the hosts who deservedly rifled themselves ahead.
The Light Blues baited the visitors as they looked to play their way out of defence, with Liam Scales hurried into an errant pass which allowed Nico Raskin – wearing the captain’s armband – to pinch possession and feed a delicious lay-off into the path of Hagi who dispatched a sumptuous driven effort into the bottom corner from 20 yards out.
Buoyed by the Ibrox crowd, the Gers had all the momentum in the opening exchanges and it was almost rewarded with a second goal of the afternoon when Cerny sprung forward on the counter-attack and had a rasping effort deflected onto the crossbar by Scales.
The away side were struggling to deal with the wave of Gers attacks, counting their fortune on 17 minutes when, again, Ridvan was able to capitalise on a loose pass and advance into the final third, although his resulting effort was comfortably smothered by Kasper Schmeichel.
It spoke to Rangers’ superiority in the contest that Kelly was effectively a bystander in the first half, with the away side unable to get their attacking trident into the game.
Every foray into the Gers half from the visitors provided Clement’s side with the opportunity to sprung forward, which they did to great effect seven minutes prior to the interval when Bajrami delayed his pass just in time to slip Mohamed Diomande beyond the defence. Carter-Vickers, however, was well-placed for Celtic.
The away side were able to sting the palms of the hitherto untroubled Kelly on the stroke of the half-time interval when Hatate struck first-time after a free-kick was cleared only as far as the Japanese midfielder.
Celtic had the ball in the net inside seven minutes of the second half when Kyogo Furuhashi latched onto a clipped pass from Paulo Bernardo and lifted his finish over Kelly, but the linesman swiftly raised his offside flag to curb any celebrations from the visitors.
Rangers, though, were unperturbed, and they ought to have doubled their advantage just shy of the hour-mark when a perfectly-timed challenge from Diomande retrieved possession and, two passes later, Cerny was denied by the inside of the far post with only Schmeichel to beat.
The Czech certainly didn’t allow the opportunity to bother him, going close once more on 64 minutes when he squared up substitute Alex Valle and forced Schmeichel into a smart stop at his near post.
From the resulting corner, Rangers doubled their advantage. It was no more than they merited.
A near post delivery was met by Raskin in acres of space and, when his diving header was blocked on the goalline by Adam Idah, the ball fell kindly to Robin Propper who slammed home his first Rangers goal from point-blank range.
The visitors were struggling to live with the Gers’ energy; Ridvan going close to adding a third of the afternoon with a dipping effort moments later.
And it got even better for Rangers before full-time when, with ten minutes remaining, Jefte swept menacingly forward and his pull-back ricocheted off Carter-Vickers and into the path of Danilo who swept home on his left side to seal all three points.
RANGERS: Kelly, Ridvan, Sterling, Propper, Jefte (Fraser, 90), Raskin (Barron, 90), Diomande, Bajrami (Danilo, 79), Cerny, Hagi (Cortes, 90), Igamane (Dessers, 90)
Subs not used: Munn, Matondo, Dowell, King
CELTIC: Schmeichel, Johnston, Carter-Vickers, Scales, Taylor (Valle, 63), McGregor, Hatate (Engels, 74), Bernardo (McCowan, 63), Kuhn, Maeda, Furuhashi (Idah, 63)
Subs not used: Sinisalo, Trusty, Palma, Yang, Ralston