Rangers 3-0 Aberdeen
Stephen Hughes celebrates his goal
Rangers made heavy weather of a match that was, for long periods, a procession towards the Aberdeen goal.
Stephen Hughes eventually made the breakthrough with under 15 minutes remaining.
Aberdeen had earlier been reduced to 10 men when Zander Diamond was dismissed for a professional foul on Michael Mols.
Peter Lovenkrands added two late goals, heading home from Chris Burke's inviting cross and then knocking in from close range after a mistake by Aberdeen keeper David Preece.
Having run Rangers close on the previous two occasions the sides met, Aberdeen set out their stall to have a go at their hosts, applying some good early pressure, with a Scott Booth header calling Stefan Klos into action.
With Craig Moore and Zura Khizanishvili missing from the home defence, the visitors would have been encouraged by a lack of organisation in Rangers' back four.
Nevertheless, it was Preece who was next into action, comfortably holding a Michael Ball free kick.
Hughes saw an effort from the edge of the box sneak just wide after 17 minutes and then Michael Mols tested Preece from 16 yards, but the keeper was equal to the task.
Rangers were finding it difficult to get in behind the Aberdeen defence, although they did have the ball in the net after 32 minutes through Shota Arveladze, only for Hughes, who supplied the cross, to be ruled offiside.
Two minutes later, Preece kept the scoreline blank with an amazing reaction save with his feet from Mols' close-range effort.
Preece was the hero again when he got a fingertip to Mikel Artera's wicked free kick to tip it onto the post.
Peter Lovenkrands celebrates the first of his goals
Rangers kept up the pressure at the beginning of the second half and as Arveladze broke through on goal after 55 minutes, he was taken out of the game by Diamond, leaving referee Willie Young no option but to show the young defender the red card.
Burke, introduced at half time, was creating problems for Aberdeen and a ball flashed across goal by the youngster deserved a taker.
The Rangers fans' frustrations were growing and things could have got worse had Leigh Hinds' long-range effort not been stopped by Klos after 69 minutes.
Arveladze should have done better than to shoot wide from inside the area following a corner but he provided the opening goal with an inch-perfect cross for Hughes to head past the helpless Preece after 77 minutes.
Moments later, Preece pulled off another fabulous save to deny Arveladze who got his head to an excellent Burke cross.
Arveladze almost got lucky late on when his shot took a wicked deflection that saw the ball spin just wide.
Then Lovenkrands added a late double, heading Burke's cross emphatically past Preece and then capitalising on a fumble by the keeper to put a flattering edge on the scoreline.
Rangers: Klos, Ricksen, Berg, Ball, Vanoli, Hughes,
Emerson (Burke 45), Arteta (Ostenstad 71), Arveladze, Mols,
Subs Not Used: McGregor, Ross, Smith.
Aberdeen: Preece, Rutkiewicz, Anderson, Diamond, Morrison,
Clark, Deloumeaux, Heikkinen (Tiernan 87), Muirhead, Booth,
Hinds (Mackie 81).
Subs Not Used: Robertson, Sheerin, McNaughton.
Sent Off: Diamond (55).
Booked: Deloumeaux, Anderson, Morrison.
Ref: W Young