The visitors will count themselves very unlucky not to have taken all three points. Particularly during the first half where their midfield trio of Kevin Thomson, Pedro Mendes and Steven Davis passed Aberdeen off the park.
Yet, despite scoring first through David Weir, they contrived to pass up several excellent chances to put the game beyond Aberdeen.
The home side drew level just before the interval through a Derek Young goal, with their first meaningful chance on goal.
After the break the game became more scrappy with neither side able to take control of the match. The Dons did have a huge let-off in the final minute of the match when DaMarcus Beasley struck what seemed to be the winner, only for the goal to be wrongly chalked off for offside.
Rangers threatened as early as the third minute when Thomson found Nacho Novo who slipped away from Andrew Considine, but from 16 yards his left-foot effort sailed narrowly over the crossbar.
Minutes later Mendes snatched at a loose ball on the edge of the area, the midfielder lacked composure and his strike flew well wide.
Aberdeen's first effort on goal came on ten minutes, Lee Miller was fouled by Madjid Bougherra. From the resulting free-kick Charlie Mulgrew's shot was on target but comfortably held by Allan McGregor.
With the visitors very much in the ascendancy they deservedly went ahead on 24 minutes. A Thomson flighted free-kick into the area was met by the visitors captain Weir, his downward header from eightyards gave Jamie Langfield no chance.
Aberdeen nearly conceded a second goal on 27 minutes. A sweeping counter-attacking move when Kris Boyd latched on to a Novo throughball, thankfully for the home side Langfield was equal to the task, getting down brilliantly to hold the big striker's shot.
The Dons stunned the visitors with an equalising on the stroke of half-time. A deep Mulgrew cross found the head of Lee Miller, his effort was brilliantly parried by McGregor, only for Young to react quickest to smash the ball home.
Aberdeen came out the far more determined side in the second half however it was still the visitors who were creating the better chances. Novo cleverly turned away from Richard Foster, before driving into the penalty area, but he stabbed a right-foot effort just wide of the upright.
Rangers' pressure was gathering some momentum and from a Sasa Papac cross Langfield had to be lively to block the downward effort from Boyd and Scott Severin clearing the danger.
On 72 minutes a neat head flick from Miller saw Darren Mackie beat Bougherra to the ball only for McGregor to get down bravely to save at the striker's feet.
Rangers thought they had grabbed a vital late winner after an excellent throughball from Davis found Beasley who slotted the ball home before turning away to the visiting fans in celebration. However the linesman's flag ruled the effort out.