A Stefan Gartenmann goal had the visitors ahead at the break before they doubled their advantage through Jamie McGrath.
Abdallah Sima found the target for Rangers with 15 minutes remaining, but Jack MacKenzie secured the points for Aberdeen with a late goal.
There was just one change to the team that defeated Livingston in the Viaplay Cup on Wednesday evening with Cyriel Dessers coming into the starting line-up in place of the injured Kemar Roofe.
Butland started between the sticks, with a back four of James Tavernier, Connor Goldson, Ben Davies and Ridvan.
Jose Cifuentes, John Lundstram and Ryan Jack were in midfield, with Abdallah Sima and Sam Lammers providing the support for striker Cyriel Dessers.
The club welcomed personnel from the Army, Royal Navy and Royal Air Force to the match for the annual Armed Forces Day celebration which recognises and honours the sacrifice of the servicemen and women.
Prior to kick-off two RAF servicemen abseiled from the Sandy Jardine Stand, before delivering the ball to the match referee Steven McLean.
An early chance for Rangers inside the opening three minutes at Ibrox saw captain James Tavernier pick out the run of Dessers but the striker was unable to keep his effort down as it drifted over the bar. It was a good start from Beale’s men as Sam Lammers dragged a low shot just wide after neat footwork to create an opening just inside the box before Sima came close with a headed effort.
With 20 minutes played, Roos pulled off a fantastic save from close range as he denied Dessers an opening goal. It was a lovely delivery into the box from Ryan Jack, with the Nigerian international rising to head towards goal but the Aberdeen number one matched the attempt with a good block.
Despite the early chances from Rangers in this match, it was the visitors who took the lead from a corner with 38 minutes on the clock. The ball was delivered into the box with Stefan Gartenmann unmarked at the back post to slot home beyond Jack Butland.
With five minutes added on at the end of the first-half, Dessers had a chance to level as he got on the end of a Ridvan cross but it was wide of the target as Aberdeen went in at the break with the advantage.
Beale made two changes at the break as Scott Wright and Borna Barisic were introduced in place of Ryan Jack and Borna Barisic.
Barisic tested Roos in the Aberdeen goal as Rangers were looking for a route back into the game. The ball was played along the edge of the box before reaching Barisic on the left, the Croatian drilled a low shot towards goal which Kelle Roos blocked.
At the other end, from a corner in the 56th minute, Aberdeen came close to getting a second at Ibrox. A ball into the box from Jamie McGrath met the head of Bojan Miovski at the back post but he was denied by the woodwork.
The second goal did come for Aberdeen as Jamie McGrath fired home a rebound shot from inside the box.
Rangers were reduced to 10 men with 20 minutes of the game remaining as MacLean showed Scott Wright a second yellow card.
With 75 minutes played at Ibrox, Rangers had a lifeline in this game as Borna Barisic delivered the ball into the box in search of Jose Cifuentes and James Tavernier at the back post. Roos was unable to clear for Aberdeen as Cifuentes got a touch to put the ball back across the face of goal, with Abdallah Sima on hand to tap home from close range.
However, with five minutes of the game remaining, Aberdeen found the target again as Hayes shot was blocked superbly by Jack Butland, but Jack MacKenzie followed up on the rebound to restore Aberdeen’s two goal advantage.
RANGERS: Butland, Tavernier, Goldson, Davies, Ridvan (Barisic, 46), Lundstram, Cifuentes, Jack (Wright, 46), Lammers, Sima, Dessers (Lovelace, 84).
Subs: McCrorie, Souttar, Sterling, Balogun, Rice, McKinnon.
Aberdeen: Roos, Devlin, MacKenzie, Shinnie, Jensen (MacDonald, 89), Gartenmann, McGrath, Miovski (Duk, 79), Clarkson (Barron, 84), Polvara (Hayes, 79), Rubezic.
Subs: Doohan, Gueye, Solker, Dunpcan, Milne.