In the sixteenth minute, Andreas Mayer found space wide on the left, and his cross found Norwegian playmaker Cato Guntveit, who rose to head the ball past Klos and make it 1-0. Countryman Arild Stavrum was on hand if Guntveit had failed to connect.
Not long after that, Rodney Wallace had the ball in the net for Rangers after a mix-up in the Dons defence involving recent Scotland call-up Russell Anderson, but it was chalked off for offside after the linesman had alerted the attention of referee Dougie McDonald.
The visitors' equaliser saw Kanchelskis instrumental in the build up with the ball ending up with Scotland midfielder Barry Ferguson hitting a deflected shot past the helpless Jim Leighton.
Shortly afterwards, a Lorenzo Amoruso free kick forced Leighton into a superb save, even more impressive as the veteran goalie didn't see the ball untill the last possible moment.
Further chances for Rangers fell to Kanchelskis, Wallace and Ferguson, but the Dons defence stood strong, with Anderson clearing one chance off the line, to hold on at the interval.
The Dons were fired up after the break and matched the champions elect in every department. Andreas Mayer, Arild Stavrum and Eoin Jess all went close for the home team with the last named in particular enjoying a real purple patch.
The Dons were also denied a certain penalty when Arthur Numan clearly controlled the ball with his hand inside the box.
The Dons made a double substitution with a quarter on an hour remaining with Rachid Belabed and Robbie Winters on for Andreas Mayer and Andy Dow. With a couple of minutes left Darren Young came on for Arild Stavrum.
Aberdeen ended the game a little disappointed that they only had a share of the spoils to show for their efforts but this was most definitely their best showing for a long time, particularly in that second half.