After a goalless first half when each team had a man ordered off, Rangers finally made the breakthrough when Richard Foster put through his own goal.
Kenny Miller added the second for the home team shortly after with a glancing header.
Any thoughts Rangers had of improving their goal difference disappeared when substitute Michael Paton pulled one back for the visitors.
In the end it was Rangers who looked out on their feet as Aberdeen pushed for an equaliser.
The visitors dominated the opening stages but then had Charlie Mulgrew sent off after a clash with Kyle Lafferty.
Mulgrew had won the foul after Lafferty's rash challenge but then he appeared to headbutt the Rangers player, although contact looked minimal.
Rangers tried to take advantage of the additional man and Sasa Papac was unlucky to see his flick from Steven Davis' shot come back off the post.
Rangers were also reduced to ten men when Madjid Bougherra was sent off for raising his boot at keeper Jamie Langfield as he went for a loose ball in the box and again it looked a harsh decision.
Neil Alexander pulled off a superb save to deny Peter Pawlett as the winger's shot headed for the top corner.
At the start of the second half, Langfield saved well from Miller before tragedy struck for the Dons.
Miller's cross was diverted into the net by Foster as the wing-back attempted to clear.
Worse was to follow for Aberdeen as Nacho Novo's corner was headed home by Miller from close range.
The visitors went close when Gary McDonald's shot grazed the bar before they did manage to reduce the arrears.
From McDonald's cross, Paton wrong-footed David Weir and Steven Whitaker before sliding the ball home.
Former captain Barry Ferguson came on after an hour to a great reception from the home fans, before John Fleck and Novo missed chances to put them further ahead in the closing minutes.