The contest was cracked open in the first-half through Tochi Chukwuani as he netted his first league goal in Rangers colours with a terrific finish from the edge of the penalty area.
Mikey Moore, outstanding throughout once again, then doubled his side’s advantage shortly into the second period, but proceedings promised to get nervy when Dennis Geiger reduced the arrears minutes later.
However, the Gers flexed their muscles and restored their two-goal cushion on the hour-mark when Nico Raskin volleyed home, before James Tavernier added the finishing touches in stoppage time with a supreme free-kick which will surely be among the club's Goal of the Season contenders.
Danny Röhl named just the solitary change to his side from last weekend’s 1-0 win in Paisley, with Thelo Aasgaard introduced in place of Djeidi Gassama.
Stephen Robinson was appointed Aberdeen boss earlier this month and began his tenure in the dugout with a 1-1 draw at home to Falkirk last time out.
His last visit to Ibrox came as recently as December 30th with St. Mirren, with Rangers forced to work ever so hard for a 2-1 victory that evening.
Indeed, it took until the ninth minute for the home side to fashion their first threat at the Aberdeen goal when a dangerous James Tavernier corner was met at the front post by Youseff Chermiti but nodded agonisingly wide of the target.
Rangers’ most menacing moments in the opening exchanges came from dead ball situations as Tuur Rommens lofted in a free-kick delivery which was cleared only as far as Aasgaard who watched his rasping effort cannon against the upper body of Ante Palaversa.
Chermiti then perhaps ought to have done better when Nico Raskin lifted a delicious pass over the top of the Aberdeen defence in search of the Portuguese, but after taking the ball in his stride wonderfully he could only steer his finish into the side netting.
For all of Rangers’ control of the contest all that was missing was the necessary quality to unpick a stubborn Aberdeen rearguard, which eventually arrived nine minutes before the interval.
The move was initiated when Raskin sent a crossfield pass in search of Rommens who showed tremendous persistence near the byline to outmuscle Dylan Lobban and pick out Moore inside the penalty area.
The on-loan winger struck first-time, but after watching his effort ricochet off Liam Morrison the ball fell invitingly to Chukwuani 20 yards out who opened up his body and planted a lovely side foot finish into the bottom corner and out of the reach of Dimitar Mitov.
Ibrox suddenly burst into life as Tavernier shot just over from distance after being teed up by Moore, before the 18-year-old showed terrific footwork moments later to dance free inside the penalty area and force a desperate Aberdeen block inside the danger area.
The hosts continued to swarm forward in search of a second before the interval, and it looked promising when Tavernier was released down the right-hand side following a sharp move but the captain was denied by a sprawling save from Mitov.
Any hopes from Aberdeen that the half-time pause would kill Rangers’ momentum were quelled inside two minutes of the second period when the hosts doubled their advantage.
An attack from the away side broke down when Raskin pinched possession from substitute Toyosi Olusanya, immediately finding Ryan Naderi who burst into space.
The German had options to his right and left, electing to use Moore who chopped back inside neatly inside the penalty area before curling a pinpoint finish into the far corner.
Robinson’s side had been reduced to virtually nothing in the contest, but they hauled themselves back into the contest with one of their first attempts at Jack Butland’s goal when Rangers played themselves into trouble in their own defensive third and Geiger capitalised to slide a finish beyond the Gers goalkeeper.
However, it spoke volumes of the Gers’ attacking intent that, just eight minutes later, they restored their two-goal advantage.
They had threatened from set-piece situations all evening, and it was another wicked Tavernier delivery, earned after the captain was scythed down by Palaversa, which wreaked havoc in the Aberdeen penalty area and broke kindly for Raskin to catch sweetly on the volley and crash home his side’s third of the evening.
Oliver Antman, Connor Barron and Jayden Meghoma entered the fray in the final quarter of the contest as Aberdeen briefly threatened when substitute Marko Lazetic crashed an effort into the side netting from a tight angle.
There was a nice combination between Naderi and Antman on the right-hand side, but the towering German couldn’t quite generate enough power on his header to trouble Mitov.
Bojan Miovski thought he had added a fourth of the evening off the bench when he slammed home, yet VAR offered his former employers a reprieve when they advised the referee to take a trip to the pitchside monitor and it was later adjudged that Barron had handled the ball in the build-up.
However, a fourth arrived all the same when Tavernier stepped up with the final action of the game and bent home a supreme free-kick which dropped in off the underside of the crossbar.
RANGERS: Butland, Tavernier, Djiga, Fernandez, Rommens (Meghoma, 80), Raskin, Chukwuani (Barron, 80), Moore (Gassama, 84), Aasgaard (Antman, 72), Naderi, Chermiti (Miovski, 84)
Subs not used: Kelly, Souttar, Sterling, Diomande
ABERDEEN: Mitov, Geiger, Bilalovic (Olusanya, 45), Nisbet (Lazetic, 65), Palaversa (Shinnie, 65), Molloy, Milne, Morrison, Aremu (Keskinen, 65), Lobban (Jensen, 45), Gyamfi
Subs not used: Bratveit, Frame, Nilsen, Armstrong