Kari Arnason opened the scoring in the second half, before Maurice Edu levelled four minutes later but neither side had the cutting edge to claim the winner.
The result was not enough for the Dons to end a wait of more than two decades for a win at Ibrox but they would have headed back to Pittodrie the happier of the two sides with the outcome.
Rangers made just one change from last week's win over St Johnstone, with goalkeeper Allan McGregor recovering from a thigh injury to reclaim the gloves, meaning Neil Alexander was back on the bench.
The Dons drafted Rory Fallon and Josh Magennis into the side in place of Andrew Considine and Mohamed Chalali, while Rory McArdle passed a late fitness test to start.
Nikica Jelavic - the subject of talks between Rangers and West Ham, as well as fresh speculation linking him with Liverpool - had a decent chance to open the scoring in the first couple of minutes.
The home side forced an early corner, which was whipped into the box by former Dons winger Sone Aluko, but the Croatian was off target with a header that dipped just over the crossbar.
At the other end, Ryan Jack slotted into the path of Magennis but his tame shot was comfortably collected by McGregor in the Rangers goal.
Rangers' best chance so far came when a header from Jelavic was pushed onto the crossbar by goalkeeper Jason Brown, before David Healy sent a thunderous effort across goal and past the post.
Aluko then forced his way past the Dons goalkeeper in the six-yard box but McArdle hooked to safety before Aluko could unleash the close-range shot and open the scoring against his previous team.
Rangers continued to push forward in search of the breakthrough before the interval and Edu teed up the shot for Lee Wallace but his effort swerved past the upright.
Former captain David Weir made a farewell appearance on the pitch at half-time and was presented with a commemorative gift from chairman Craig Whyte to mark his service to the club over the last five years.
Once the second half was under way, Aluko threaded into the path of new skipper Steven Davis and he delivered a teasing ball into the box but a full stretch Jelavic could not find the target.
A corner from Aluko then found Dorin Goian in the packed goalmouth but the big defender failed to keep his header down and the effort fell over the crossbar.
The Dons had a great chance of their own when McGregor fumbled a corner and Carlos Bocanegra cleared off the line but the visitors were ahead after 63 minutes when Arnason met a Chris Clark ball and curled past the Rangers goalkeeper.
The Scottish champions were back on level terms just four minutes later when the ball broke for Edu to rifle high into the top corner of the net.
Rangers had received a massive lift from the equaliser and Edu could have grabbed his second of the day with less than 10 minutes to go.
The American midfielder raced onto a great pass from Jelavic before producing a well-struck shot that whistled inches past the post.
Kyle Bartley then bulleted a header over from a Gregg Wylde cross and Aluko forced a superb save from Brown but Rangers could not find the winner.