The visitors were reduced to ten men on 37 minutes when Lee McCulloch saw red, but they still carved out at least four excellent chances which should have seen them pick up three vital points in an ever-tightening title race.
Aberdeen seemed to have suffered a Euro hangover as they failed to impose themselves at any stage during the 90 minutes.
After a poor opening ten minutes, Aberdeen came close when Scott Severin fed the ball to Ricky Foster who broke clear of Steven Whittaker before laying the ball wide to Jamie Smith, but his fierce drive from the angle of the box just wide of the upright.
On 14 minutes Steven Naismith got his head to a long Alan Hutton cross but Jamie Langfield did very well to hold the effort at the second attempt.
Naismith was proving a thorn in the Aberdeen defence and on 18 minutes he drove to the byline, picking out Daniel Cousin with a great cross, however, the striker carelessly blazed his effort wildly over the crossbar.
The visitors' dominance was rewarded on 30 minutes with a sweeping move.
Hutton fed the ball through to McCulloch who carried it into the area before sweeping across the six-yard box for the on-rushing Charlie Adam to gleefully drive home.
Minutes later Adam fed Naismith running through the channel and only a tremendous finger-tip save from Langfield prevented the diminutive striker from doubling the advantage.
Aberdeen undeservedly drew level on the stroke of half-time.
Rangers failed to clear a Barry Nicholson corner and the ball fell to Richie Byrne, who drove back into the six-yard box where Lee Miller headed home.
Immediately from the restart, Cousin turned Byrne inside the area, but from a tight angle he failed to hit the target rather than cut back to strike partner Naismith, who was the better option.
On 64 minutes Aberdeen centre-back Byrne was caught in possession and lost the ball to Naismith.
His early ball caught the Dons defence square, allowing Cousin to race into the area only for Langfield to brilliantly block the big striker's effort.
Rangers passed up another good situation on 76 minutes when second-half substitute Kris Boyd ran onto a clever ball from Naismith only to screw his effort wide of goal from 16 yards.
Rangers again went close on 80 minutes when Naismith skipped past Lee Mair before driving the ball into the six-yard box where the ball deflected off the outstretched leg of Zander Diamond and onto the crossbar.