It was night of major frustration for Rangers' captain Barry Ferguson
Aberdeen ended Rangers' last-day SPL championship challenge with a win at Pittodrie, as Celtic retained the title with victory at Dundee United.
Dons keeper Jamie Langfield made smart first-half saves from both Carlos Cuellar and Jean-Claude Darcheville.
Aberdeen went ahead when Lee Miller headed home in the 63rd minute from an inch-perfect Barry Nicholson free-kick.
Darren Mackie added a second after 76 minutes before Rangers' Nacho Novo was dismissed for a lunge on Stuart Duff.
Aberdeen's industry was impressive and, with Hibernian losing to Motherwell, Jimmy Calderwood's men claimed fourth place in the table.
For Rangers, it proved to be a night of deep frustration, the second of the four prizes available to them slipping away, with the Scottish Cup final against Queen of the South to follow on Saturday.
The Light Blues headed into the customary tough test in the Granite City hoping leaders Celtic would slip up at Tannadice, with the title race reaching epic proportions.
Manager Walter Smith made three changes to the side that defeated St Mirren 3-0 at Love Street on Monday.
Daniel Cousin was selected to partner Darcheville up front, while Charlie Adam and Cuellar were also included.
And the Ibrox side were first to show real intent after eight minutes.
However, Steven Davis could only scuff his shot when presented with a chance from close range from a Darcheville pass, before Langfield made an excellent reflex stop from a Cuellar drive inside the box.
With the game in full effect, Maguire volleyed over for Aberdeen from 20 yards after Steven Whittaker was dispossessed, much to the relief of the Rangers defender.
Langfield proceeded to palm away a Darcheville drive on the counter-attack, while Stuart Duff drove a shot inches wide for the Dons with both sides displaying a tangible sense of urgency.
Barry Ferguson - who had been impressive in midfield - should have done much better when set up by the industrious Darcheville, but the Ibrox captain blasted the ball well over from a good position, before Adam passed up a set-piece from 20 yards out.
Lee Miller (left) heads home Aberdeen's opening goal at Pittodrie
And, with the deadlock unbroken at the interval, the visitors still required an elusive goal to put pressure on Celtic, who also went in at 0-0 at Tannadice.
Aberdeen almost caught Rangers cold two minutes into the second half, but Neil Alexander stood firm to deny a powerful strike from Nicholson.
Rangers responded with Ferguson fastening on to an inviting Darcheville pass but his finish lacked power and Langfield gathered.
Smith sent on Kris Boyd and Nacho Novo for Darcheville and the lacklustre Cousin respectively, but it was the Dons who immediately ignited matters with Miller's goal.
Nicholson flighted in a free-kick and Miller rose between Rangers defenders to glance home a textbook header, beyond the reach of Alexander into the corner of the net.
The outcome was put beyond any doubt when Miller headed an inviting ball into the path of Mackie, who edged past Cuellar to force the ball past the exposed Alexander.
Frustration got the better of Novo with the striker lashing out late on Stuart Duff, the Spaniard now missing the Hampden showpiece as a result.
With the title remaining at Celtic Park on a night of drama, Rangers now have to turn all their attention to securing a cup double - while questions will be asked of precious points dropped in the title run-in.
Aberdeen: Langfield, Maybury, Severin, Diamond, Foster, Maguire (Jamie Smith 69), Nicholson (Young 88), Touzani, Duff, Miller, Mackie (De Visscher 83). Subs Not Used: Soutar, Mair, Crawford, Jack.
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