Sitting on a one-goal lead from last week's first leg, Derek McInnes's men had to ride their luck late on in order to set up a meeting with Croatian outfit Rijeka in the second qualification round.
The first real opening of the game fell the way of Armend Alimi, who was unable to guide his effort on target after a smart piece of build-up play.
Both sides enjoyed spells on the ball, but chances proved to be few and far between as the scoreline remained locked following the first leg in Macedonia.
Adam Rooney felt that he should have been awarded a penalty in the closing stages of the first half after being brought down, but the referee was quick to wave play on.
Only a fine challenge denied McLean racing through on goal, although Shkendija were also creating opportunities of their own as Alimi troubled Danny Ward between the sticks.
The Dons looked to have won it with 10 minutes remaining when Peter Pawlett's dipping shot from range was only kept out by the crossbar, before Blagoja Todorovski squandered a double chance up the other end.
All the pressure was on the visitors to find a late goal, however, and they very nearly did so when Agim Ibraimi got a shot away at goal, but Ward was equal to the effort to ensure that the hosts moved a step closer to the group stages.