The Bairns, who have not won at Pittodrie since 1958, fell behind on Saturday when Miller coolly netted from the penalty spot, and the striker grabbed a second against his former club shortly before half-time.
Falkirk dominated the second half and Steve Lovell grabbed a consolation before the end but the Dons held out for their fourth consecutive home win.
Chris Maguire and Jeffrey de Visscher both started against Falkirk in an attack-minded Aberdeen side on a wet and wild day in the Granite city.
The Bairns made three changes to the side that lost 2-1 to St Mirren last weekend.
Gerard Aafjes replaced the suspended Jackie McNamara, while Graham Barrett and Scott Arfield came in for Arnau Riera and Patrick Cregg.
Aberdeen almost took the lead in the fifth minute when Lee Mair’s cross looked to be heading into the net after it deflected off Falkirk skipper Darren Barr but goalkeeper Robert Olejnik did brilliantly to tip the ball out for a fruitless corner.
Zander Diamond should have opened the scoring but he headed over the bar after Olejnik slapped at a Charlie Mulgrew corner.
Burton O’Brien then brought the best out of Jamie Langfield in the Aberdeen goal with a curling effort from 30 yards after 11 minutes.
However, it was the home side who took a deserved lead from the penalty spot. Dutchman Aafjes brought down Gary McDonald in the box and Miller coolly dispatched the ball past Olejnik from 12 yards.
Aafjes was booked for his challenge on McDonald and Kevin McBride followed him into the referee’s notebook soon after.
Falkirk were denied a penalty of their own when Barrett looked to have been clipped by Langfield after 38 minutes.
But as the away side looked to have weathered the storm, they found themselves two down when Miller notched his second of the day.
The Dons striker stretched to divert an inviting Maguire cross past Olejnik after 42 minutes for his fifth goal of the season.
He could have netted his hat-trick just before half-time but Falkirk keeper pushed his drive over the bar.
Falkirk started the second half strongly, with Arfield testing Langfield from distance.
The away side continued to dominate proceedings, with captain Barr heading over an O’Brien corner that had been needlessly conceded by Langfield.
Lovell then almost grabbed one back against his former club, but his effort was diverted wide by Scott Severin.
Aberdeen responded to an awkward onslaught by making a double substitution after 70 minutes, with Derek Young and Richard Foster coming on for Maguire and De Visscher.
The home side began to regain the initiative but McDonald and Darren Mackie both failed to hit the target from promising positions.
Bairns boss John Hughes brought on another striker, with Mark Stewart replacing McBride with less than 10 minutes remaining.
Lovell lashed the ball into the corner of the net with clinical precision to set up a tense finale but the Dons held on for all three points.