Gers boss Alex McLeish will be delighted with his side's performance in which Dado Prso and Barry Ferguson were in outstanding form.
On the other hand, Jimmy Calderwood will be asking questions of his Dons players, who didn't seem up to the battle despite a European place still being within their grasp.
On four minutes Alex Rae and Ferguson combined before the latter drove in a fierce effort which was held by Ryan Esson.
At the other end, minutes later a Scott Muirhead free-kick to Scott Severin saw the midfielder narrowly off target with his 30-yard shot.
Rangers took a deserved lead after ten minutes with a cleverly worked goal. Prso chased a long headed clearance from Marvin Andrews before turning inside Ritchie Byrne and finding Ferguson, whose left-footed effort from 18 yards flew into the net.
Aberdeen almost got back on level terms when Kevin McNaughton released Muirhead wide on the left. His high looping cross caused panic in the Rangers rearguard before the ball dropped to Zander Diamond, but Sotirios Kyrgiakos was on hand to charge down the centre-back's effort.
Prso again figured prominently in Rangers' front line, creating space for himself before firing in a low drive which was easily held by Esson.
A clumsy challenge by Russell Anderson on Prso at the edge of the area on 25 minutes almost led to a second goal for the visitors. From the resultant free-kick a swerving Ferguson effort was brilliantly parried over the crossbar by Esson.
A lightening quick break by Ferguson picked out Peter Lovenkrands whose early ball into the Dons box saw Byrne bravely block a Nacho Novo shot.
Aberdeen nearly got an unlikely equaliser on 31 minutes when Maurice Ross slipped when going for the ball, allowing Darren Mackie a sight of goal. But the young Dons striker passed up the opportunity, choosing to cross instead of shooting.
The Dons were back on level terms after 33 minutes when Chris Clark picked up a loose ball 30 yards out, sidestepped away from Rae before crashing in a great drive which took a slight deflection off Andrews and flew past the hapless Ronald Wattereus.
Aberdeen briefly took control and Severin tested Wattereus, but the big Rangers goalkeeper got down the save comfortably.
Rangers forced a corner on 41 minutes but Prso's acrobatic overhead kick went high and wide of goal.
In the final minute of the half Rangers scored an exquisite second goal. Novo beat Byrne and Anderson on the right before picking out Prso, whose cute back heel found its way past Esson and into the corner of the net.
Aberdeen pressed after the re-start but all too often their final ball into the area didn't have enough quality to trouble the visiting centre-backs.
Rangers put the result beyond doubt after 59 minutes. A Fernando Ricksen corner was headed on by Andrews and dropped at the feet of Prso, who had time to take a touch before wheeling round and driving the ball high into the net from six yards out.
The Gers were rampant at this stage and only a fantastic fingertip save by Esson stopped Ferguson increasing the visitors' lead.
Andrews almost scored a fourth in the 76th minute when a swerving free-kick from Ferguson found him towering above his marker to get his header on target, which Esson did well to gather at his left hand post.
On 88 minutes a superb stop by Esson foiled Steven Thompson, who should have netted when presented with an excellent chance from a Shota Arveladze cut back.
As the game entered stoppage-time Ferguson raced onto a Thomas Buffel throughball only to be denied by the woodwork, the ball ricocheting away to safety.