After a first half that Rangers dominated for long spells but just couldn’t find the net, Barry Robson’s side took the chances that came their way in the second period, with defender Liam Scales and striker Bojan Miovski getting the goals on 48 and 56 minutes respectively.
With Pittodrie packed and the home support in high spirits after watching their in-form side win six league games on the bounce to move up into third, it was Rangers that started the match on the front foot, with most of the players in blue getting early touches on the ball.
Aberdeen, with their fans driving them on, gradually got into the game but they were lucky not to be a goal down as the visitors asked questions of their backline.
With just 12 minutes played, a deep cross from James Tavernier was nodded down by Fashion Sakala and Alfredo Morelos, with his back to goal, turned and shot but Leighton Clarkson was there to block his effort on the line.
Sakala was proving a handful with his pace and when Malik Tillman produced a defence-splitting pass to the Zambian he was one-on-one with the home side’s goalkeeper Kelle Roos who made an impressive – and important - save to keep the score goalless.
Rangers, wearing their all-blue kit, certainly looked the more likely of the two teams to break the deadlock and on 25 minutes they came within inches of doing just that.
Tillman fed a clever pass to Borna Barisic who was unmarked as he made an overlapping run into the box. The Bosnian hit a left-foot shot first time and the ball clipped the outside of Roos’ near post before going out for a goal kick.
At the half-hour mark Beale’s men were dominating play with Allan McGregor not yet having a save to make. Aberdeen, meanwhile, were under pressure from Rangers’ attacking play.
Next up to push forward into the Dons’ 18-yard box was Nico Raskin, who received a delightful, flicked pass from Sakala but the Belgian’s shot was brilliantly blocked by Mattie Pollock.
Before half-time McGregor was called into action. A slack pass from Ben Davies allowed Ylber Ramadani to burst forward and the Gers number one had to be sharp to get down to the midfielder’s powerful drive.
Three minutes into the second half and Aberdeen opened the scoring, and while it might have been fortuitous, Liam Scales made his own luck.
The big defender was quick to intercept a pass from Tavernier to Morelos in front of the Dons’ dugout and what looked to be an attempted cross seemed to take an eternity as it floated and then dipped into the opposite top corner of McGregor’s net.
Rangers now found themselves behind and things were to get worse on 56 minutes as Robson’s men doubled their advantage.
Clarkson had space and time to deliver a teasing cross and Bojan Miovski dived to head the ball across McGregor and high into the net.
Tavernier tried to lift his stunned side - his right-foot, curling effort going inches over the bar and clipping the roof of the net. In the next attack, the Gers skipper was then denied when the ball dropped to him in the box but Roos made an instinctive, point-blank stop.
Rabbi Matondo then came so close to throwing his side a lifeline, the substitute sprinting forward and curling the ball past Roos, but it clipped the outside of the post to the despair of the Rangers fans in Pittodrie’s away end.
Eight minutes of injury time were added but this just wasn’t to be Rangers’ day and it was Aberdeen that celebrated victory at the final whistle.
ABERDEEN: Roos, McCrorie, Scales, Miovski, Lopes (Watkins 87), Ramadani, Hayes, Pollock, Clarkson, Duncan, MacDonald
SUBS NOT USED: Gorter, MacKenzie, Barron, Markanday, Myslovic, Coulson, Kennedy, Bavidge
GOALS: Scales 48, Miovski 56
BOOKINGS: Scales, Lopes
RANGERS: McGregor, Tavernier, Souttar, Davies, Barisic, Raskin (Matondo 64), Lundstram, Cantwell, Tillman, Sakala (Arfield 88), Morelos
SUBS NOT USED: McLaughlin, Yilmaz, Hagi, Kamara, King, Lovelace, Rice
BOOKINGS: Cantwell
REF: Nick Walsh