Chances were at a premium in a closely contested encounter, although United’s Australia international Ryan McGowan reacted swiftly to clear an Andrew Considine shot off the line.
But the Dons were not to be denied and McLean claimed the spoils, albeit in slightly fortuitous fashion.
The midfielder stooped to flick on a weak David Goodwillie cross and his header went in off the underside of the crossbar as German goalkeeper Luis Zwick failed to back pedal in time to claw the ball away.
Both sides struggled to establish themselves in the opening stages, although Aberdeen had the excuse of having travelled to Kazakhstan in midweek on Europa League duty.
Graeme Shinnie did go close from long range for the Dons before their keeper Danny Ward kept out a Chris Erskine effort.
McLean and Blair Spittal had shots blocked at either end but United striker Mario Bilate had the best opportunity of the half.
Aberdeen defender Paul Quinn failed to deal with a ball into the box after they struggled to properly clear a corner but Ward stood up well to block Bilate’s shot with his chest.
The second half started slowly but the game improved as a contest after the hour mark.
Jonny Hayes exchanged passes with McLean but shot wide of the near post when a ball across the goal would have caused more problems.
Ward pushed Mark Durnan’s header away from danger following Spittal’s free-kick as both managers pushed players forward in search of a winner.
Defender Coll Donaldson then headed over for the hosts but that proved to be United’s final chance of the match.
First Considine went close for Aberdeen before McLean broke the deadlock and the visitors held firm to secure an opening victory as they look to try and push Celtic all the way once again this campaign.