His 55th-minute strike was worthy of the three points alone as Falkirk won only their second league match in 14.
Aberdeen had plenty of the ball in the first 20 minutes but failed to ask any questions of Dani Mallo who was his league debut.
It took a stretch from Steven Pressley to prevent a dangerous cross from Javan Vidal reaching Miller in the area as Aberdeen tried to exert more pressure.
But it was Falkirk that almost had a chance at the other end after Higdon headed the ball on, but Scott Severin managed to shepherd the ball back to Jamie Langfield.
Falkirk had a major let-off when they failed to deal with a corner from Charlie Mulgrew and the ball broke to Severin whose fiercely-struck shot was blocked on the line by Arnau Riera.
It prompted a reaction from the Bairns and when Aberdeen were similarly troubled at a Scott Arfield free-kick, Higdon blazed a ten-yard shot over the top when he should have done much better.
Aberdeen then tore through the home defence when Stuart Duff played Darren Mackie in early but Mallo managed to push the ball away for a corner.
Mugrew's kick was met by the head of Severin but this time his effort hit Mackie in front of goal and Falkirk escaped again.
But Falkirk were not without threat. Higdon was just inches away from connecting with a teasing cross from Scott Arfield as Langfield grabbed it.
Falkirk made the breakthrough ten minutes into the second half with a quality goal. Steve Lovell sent Higdon clear and he rifled an unstoppable shot into the roof of the net to leave Langfield with no chance.
Jimmy Calderwood sent on all three substitutes in a bid to salvage it but Falkirk defended doggedly to try and hold onto the points.
They also carried threat going forward although Dean Holden was outrageously ambitious with one effort from 30 yards which finished high up in the stands behind the goal.
Lovell saw a glancing header touched away by Langfield after Scott Arfield had chased what looked to be a lost cause.
Lovell then should have settled it when he was clean through and lobbed the goalkeeper only to see the ball drift wide.