The Dons headed south desperate for a victory after a dreadful run of form and the three points will have eased the pressure on manager Jimmy Calderwood.
The home side enjoyed the lion’s share of the possession but, with ex-Pittodrie marksman Steve Lovell passing up a hat-trick of gilt-edged chances, they could not find a response to Miller’s 48th-minute header.
Lee Bullen was harshly red-carded by referee Willie Collum in injury-time at the end of the match for a supposed last-man foul on Scott Severin to complete a miserable afternoon for the Bairns.
The match, which was preceded by a minute’s applause for the late Dundee United chairman Eddie Thompson, kicked off in a swirling wind which was hardly conducive to either side’s passing game.
Aberdeen were seeking their first win since August and Falkirk their first victory over the Dons for 14 years, and it was the home side who seemed more in the mood early on.
Defender Dean Holden, making his return from nine months out with a horrific double leg break, was heavily involved in the opening stages, bombing forward from left back to provide support to the Bairns’ attacks.
And it was down the left that the home side carved out the game’s first real opportunity in the eighth minute.
Michael Higdon burst through a couple of weak challenges before sending Neil McCann scampering away down the flank.
The winger’s cross was magnificent but former Aberdeen striker Steve Lovell’s header back across goal drifted wide of the target.
Scott Flinders, drafted in for Robert Olejnik, then found himself in the spotlight on his debut as whistler Collum made two close calls.
Holden’s back pass was short in the 17th minute and the on-loan Crystal Palace keeper appeared to bring down Darren Mackie as the Dons marksman reached the ball first, only for Collum to wave play on.
Two minutes later, Lovell had the ball in the net at the other end but play was pulled back for a push on Severin in the build-up.
McCann, making his first start in almost a month because of injury, had evidently been handed a roving commission by manager John Hughes and he looked dangerous every time he got on the ball.
However, he was robbed by Andrew Considine in the 40th minute and was relieved to see the defender’s powerful drive slip just over.
Calderwood responded to his team’s first-half showing by making a change at the break, with winger Sone Aluko being introduced at the expense of Stuart Duff.
And the former Birmingham youngster was immediately involved as the Dons took the lead only three minutes after the interval.
Aluko made inroads in midfield before the ball was shipped wide to Considine and the defender’s superb cross was inch-perfect for former Falkirk striker Miller to head powerfully in from eight yards.
Falkirk were knocked out of their stride by the goal but came close to restoring parity only seven minutes later.
McCann’s low free-kick allowed Higdon to back in to his marker and turn but his resultant shot drifted across goal and wide of the upright.
Lovell, who had been quiet against his old team, then came within a whisker of an equaliser for Falkirk as he side-footed McCann’s cutback just wide.
The striker then passed up an even clearer chance in the 74th minute as Falkirk kept up their siege on the Dons goal.
McCann first lost the ball and then won it back before threading a great pass into Lovell’s feet in the inside-left channel, but the Englishman could not find the target with his poked shot.
Aluko’s pace on the break was Falkirk’s main threat in the closing stages as Aberdeen appeared content to sit in and defend their slender lead.
Dons substitute Jamie Smith curled a free-kick narrowly wide after Aluko had been brought down by Darren Barr on one such raid.
And no matter how many long balls Falkirk threw forward in the closing minutes they could not find a way through, with Bullen’s red card the final act of a desperate finale.