The on-loan Plymouth striker broke the deadlock after 12 minutes when he pounced on Davide Grassi's flick to smash the ball past Robert Olejnik.
The Bairns were unfortunate to be denied a penalty just before the break when Ryan Flynn fell in the penalty area under pressure from Zander Diamond.
But, despite dominating possession in the second half, Steven Pressley's side rarely tested Jamie Langfield in the Aberdeen goal as the Dons held on for the win - only Aberdeen's second in 16 matches - to open up a nine-point gap over bottom side Falkirk.
Aberdeen made two changes from the side that lost 3-1 to St Johnstone with Derek Young and Stuart Duff preferred to Michael Paton and Paul Marshall.
Falkirk travelled north in confident mood after back-to-back victories and were unchanged from the side that defeated St Mirren 2-1 last weekend.
After a tentative start from both sides it was the visitors who carved out the first opening after six minutes when Pedro Moutinho darted past two defenders before dragging his shot well wide of the target.
However, it was Mark McGhee's side who opened the scoring after 12 minutes. Duff, who started the match at right-back, found Grassi whose neat flick-on fell kindly into the path of MacLean to volley the ball emphatically past Olejnik.
The Dons could have doubled their advantage eight minutes later but Kieran Duffie made a brave clearance from an enticing Charlie Mulgrew delivery with Diamond ready to head the ball home.
Falkirk's Mark Stewart had a goal ruled out for offside just before the half-hour mark as Steven Pressley's side began to offer more going forward after a slow start.
MacLean should have netted a second for the hosts after 34 minutes when he latched onto a Young pass and chipped weakly past Olejnik but Brian McLean raced back to clear the ball before it crossed the line.
The visitors were furious when they were denied a penalty when Ryan Flynn fell in the box under pressure from Diamond just before the break.
Falkirk manager Steven Pressley made a tactical change during the interval with former Leeds striker Enoch Showunmi replacing the ineffective Stewart.
Darren Mackie picked up the first booking of the match after 50 minutes for a high challenge on McLean.
The Bairns had a second penalty appeal waved away when Jerel Ifil looked to have handled Moutinho's cross, although it would have been a harsh award.
Duff then joined Mackie in the referee's notebook when he cynically ended Showunmi's run down the left wing.
The visitors introduced Carl Finnigan for Moutinho just after the hour mark as they enjoyed a period of dominance.
Substitute Finnigan was replaced by Jack Compton only 11 minutes after coming on after injuring himself in an accidental collision with Diamond.
With ten minutes to go Aberdeen brought on Paton for the tiring Mackie as they looked to hang on for the victory.
Falkirk threw everything at Aberdeen in the final stages but Langfield and the Aberdeen defence held firm to ensure the three points remained at Pittodrie.