Rangers had to survive a torrid second half as an inspired Aberdeen side fought back.
A first-half goal by Michael Mols was matched when Steve Tosh pulled Dons level with 15 minutes remaining, but a second goal from the Dutchman shortly after calmed the home side's nerves, though the Dons pressed to the finish.
The home side threatened first but Mols headed weakly into the hands of Dons keeper David Preece. Then, from a suspiciously offside position, Mols was put through from a Mikel Arteta pass but Preece blocked his shot.
Both Neil McCann and Arthur Numan were delivering quality crosses from the left, but Mols in particular was failing to capitalise.
There was some Dutch magic in the 25th minute when Ronald de Boer tormented the Dons defence before curling an exquisite shot which crashed back off the post.
Aberdeen showed they were here to make a game of it when Gers keeper Stefan Klos had to pull off a great double save from Tosh and Darren Mackie.
Leon Mike was just off target with an overhead shot before the home side were denied what looked like a clear cut penalty when Arteta was brought down by James McAllister.
The home side finally made the breakthrough when Fernando Ricksen's cross, after a short corner to Numan, was headed powerfully home by Mols.
De Boer's powerful shot at the start of the second half was well saved by Preece but Aberdeen gradually assumed control and Klos did well to block a Chris Clark shot.
Mike then beat Bob Malcom easily, but could only finish weakly.
The visitors' pressure finally paid off when Tosh's powerful run into the box ended with a crisp shot low past Klos into the corner of the net.
Rangers responded quickly with de Boer's pass releasing Claudio Caniggia and after the winger cut inside Kevin McNaughton, Mols was on hand to force the ball home much to the relief of the home fans.