A Kari Arnason strike on 62 minutes gave the visitors a shock lead but Mo Edu responded quickly with a deflected equaliser in what proved to be a dramatic second half.
The Light Blues did everything they could to grab a late winner but it was not to be and the result means Celtic are now four points clear at the league summit.
Prior to kick-off the Ibrox faithful welcomed new signing Mervan Celik to the club with the Swedish under-21 international walking out into the centre circle.
But, perhaps not surprisingly, Sone Aluko did not receive a similar standing ovation from the Aberdeen fans when he jogged over to take a corner in front of them with just a minute of the game played!
Rangers enjoyed a lot of possession in the opening half hour and on 22 minutes Nikica Jelavic came close to breaking the deadlock when he climbed above Dons’ stand-in skipper Arnasen and his header was tipped on to the cross bar by Jason Brown.
The Croatian then turned provider when he flicked the ball to his strike partner David Healy who had found space on the right channel but fired his shot wide of the Welsh keeper’s near post.
On 32 minutes the game was held up as Fraser Fyvie made several attempts to place the ball down for a corner only for it to be blown away to the amusement of the Rangers supporters.
But when he finally whipped in his dangerous cross Arnason made a great run and his header skimmed off the top of McGregor’s cross bar to the relief of the Gers number 1 who had not had to make a save up to that point.
In the final five minutes Lee Wallace, Mo Edu and Healy all came close to netting the opener but at half time the game remained goalless.
The interval, however, did give three in a row captain David Weir the chance to walk down the Ibrox tunnel and bid an emotional farewell to the club and fans he has served so well for five memorable years.
Craig Brown and McCoist elected to stick with the same players for the restart as the weather deteriorated and the rain lashed down on the Ibrox playing surface.
As a result the second half had everything apart from a winning goal at the death.
On 58 minutes Arnason again connected with a Fyvie corner and with McGregor unable to get a hand to the ball his header had to be hooked clear by Bocanegra.
But after the hour mark the first goal arrived and it was a great finish from the Icelander who cut inside from the left and curled a low shot beyond McGregor, giving the keeper no chance.
The packed away end of the stadium erupted and McCoist reacted quickly by taking Healy and Lee Wallace off and replacing them with Gregg Wylde and Salim Kerkar.
The team also responded and on 66 minutes Edu’s tenacity was rewarded when his deflected shot from 20 yards found the corner of Brown’s net.
With the clock ticking down Rangers threw everything forward as they went in search of a second goal and on 80 minutes Edu had his head in his hands when his shot, following excellent wing play from Jelavic, trickled past Brown’s far post in front of the Copland Road Stand.
Aluko and Bocanegra were also denied by the keeper in injury time as Aberdeen defended for their lives to gain a vaulable point as they step up their bid to move into the top six.
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