The Irishman smashed the ball into the top corner after 31 minutes to give the Bairns a deserved win over the Dons, who offered little in attack.
Eddie May's side could have put the game beyond doubt but squandered a number of chances in the second half.
However they held on for all three points as Aberdeen slumped to a fourth defeat in their last five home league games, and now Hamilton are propping up the rest.
Aberdeen's new loan signings Steven MacLean and Jim Paterson made their debuts following the deadline-day departure of Lee Miller to Middlesbrough.
Zander Diamond was handed his first start since the opening day of the season with Derek Young and Davide Grassi dropping to the bench.
Falkirk made two changes to the side who lost 3-0 to Rangers with Kieran Duffy preferred to former Don Jackie McNamara and Carl Finnigan starting ahead of Jack Compton who missed out altogether.
Aberdeen made the brighter start but it was the visitors who could have taken an early lead when Enoch Showunmi outmuscled Jerel Ifil but Jamie Langfield gathered at the feet of the former Leeds striker.
Paterson, playing at left-back, fired over after 11 minutes before skipper Mark Kerr blasted over as the home side's pressure began to mount.
Falkirk's Brian McLean received the first caution of the game after 16 minutes for tripping Darren Mackie off the ball and Marc Twaddle joined him in the referee's notebook a minute later for a deliberate handball.
Charlie Mulgrew almost gave the Dons the lead after 23 minutes with a curling free-kick that Robert Olejnik just managed to keep out.
The Bairns picked up their third booking of the encounter after 27 minutes when captain Darren Barr was cautioned for a foul on Mackie.
Falkirk took the lead against the run of play when Finnigan laid the ball into the path of Irishman Healy who fired past Langfield from 20 yards.
The Dons should have equalised four minutes later when Paterson's corner found the head of Mackie but the striker somehow managed to head over from six yards.
Just before the break youngster Fraser Fyvie was booked for a needless pull on Portuguese midfielder Vitor Lima.
The visitors could have doubled their advantage within four minutes of the break when Twaddle headed Healy's cross into the path of McLean whose effort was blocked by Langfield.
The Dons made an early change after 54 minutes with Michael Paton replacing Fyvie who had a quiet game.
Debutant Paterson was denied an equaliser after 58 minutes when his low, right-footed drive was well saved by Olejnik.
Falkirk should have put the game beyond doubt after 63 minutes but substitute Mark Stewart failed to connect with Showunmi's enticing ball across the face of goal before Ryan Flynn was brilliantly denied by a one-handed Langfield save.
Langfield could then only parry a Lima strike from distance before Stewart fired over from inside the area as the Bairns pressed for a second.
Derek Young came on for Aberdeen in place of Paterson who looked to be suffering from cramp with 15 minutes to go.
The visitors continued to threaten on the counter-attack with Showunmi causing plenty of problems for the Dons rearguard.
The home side did muster a late rally with Young's cross-cum-shot being pushed away by Olejnik for a fruitless corner.
And with three minutes to go the Austrian goalkeeper pulled off a tremendous save to deny substitute Michael Paton to ensure his side departed with maximum points.