Rangers boss Alex McLeish will be very disappointed as his side failed to win this match after totally dominating proceedings during the first 45 minutes.
A transformed Aberdeen team roared back at the league leaders in the second period and were well worth a share of the spoils in a pulsating encounter.
After five minutes Rangers should have taken the lead. Slick play between Russell Latapy and Shota Arveladze found Michael Mols, who miskicked his shot safely into the arms of David Preece.
With 20 minutes on the clock Ronald de Boer stumbled as he moved on to a Derek Ferguson throughball and Preece reacted quickly and the danger was averted.
Not surprisingly Rangers took the lead after 23 minutes when neat link-up play between Arthur Numan and Arveladze saw the latter's shot go through a crowd of players and beyond the unsighted Preece.
Minutes later Maurice Ross' cross took him to the byline, from his deep cross Arveladze out jumped the Dons defence, only for Phil McGuire to head the ball off the line. With Rangers in total command Fernando Ricksen put Mols through one-on-one with Preece, the Dons keeper did well to block the striker's effort.
Aberdeen had their first effort on goal in 50 minutes when Russell Anderson powered in a header which was well off target.
Minutes later the best chance yet for the home side fell to Darren Mackie who drove narrowly over after Leon Mike had dispossessed Bert Konterman at the edge of the area.
With 55 minutes gone Stefan Klos produced an excellent fingertip save to push Darren Young's 25-yard effort over the bar. From the resultant corner the game was turned on its head when Mike rose to score his first league goal of the season as he nodded home from three yards.
Mackie picked out Kevin Rutkiewicz 16 minutes from time, who took the ball wide before firing the ball across the area for Mackie to gleefully head beyond Klos as the Dons took an unexpected lead.
Rangers' response was immediate when Arveladze's header from a Latapy cross was excellently held by Preece.
The Dons were only to hold the lead for four minutes as Ferguson easily converted a penalty kick following McGuire's rash challenge inside the area on Ricksen.
Right at the death Eric Deloumeaux almost gave the home side all three points, only for Klos to make a breathtaking fingertip save