The former Crewe striker latched on to a pass from partner Steve Lovell 10 minutes after the break to net the only goal of the game and stretch the Bairns' advantage on bottom side Inverness to five points.
The defeat brought to an end a run of only one defeat in nine games for Aberdeen, whose best chances fell to skipper Scott Severin on an afternoon of frustration in front of goal.
A win over Celtic and a draw with Rangers had heightened the visitors' expectations on their journey down from the north-east but it was to prove Falkirk's afternoon as they notched their first win over the Pittodrie side in 15 years.
Falkirk came into the match looking to improve on a dire record of only one win in their last 13 matches that had seen them plummet to second bottom in the SPL table.
The omens were not good, with the Bairns having failed to beat their opponents in any competition since 1994 and only twice in their last 46 encounters, but all that was to change as they finally sealed a crucial win.
Referee Euan Norris wasted no time in stamping his authority on the proceedings as he booked Falkirk full-back Dean Holden for a trip on former Bairns striker Lee Miller within the first minute.
It was a hint of what was to come in an opening spell characterised by persistent fouling, misplaced passes and a lack of cohesion from both sides.
Charlie Mulgrew, normally so accurate with his set-pieces for Aberdeen, sent a free-kick straight into Falkirk's two-man wall to waste an opportunity for the visitors.
At the other end, former Pittodrie marksman Lovell trundled a shot on target but neither goalkeeper was threatened in a poor start to the match.
Steven Pressley stretched his neck muscles to flick a Javan Vidal cross away from Miller as the game briefly came to life with Aberdeen seeking the breakthrough.
And they came close to the opener in the 23rd minute, only for Arnau Riera to clear Severin's shot off the line after a scramble prompted by Mulgrew's in-swinging corner.
Severin's opportunity ignited the game and Higdon should have done better than blast over in the 26th minute after Scott Arfield's free-kick had rebounded into his path.
In the 28th minute, Stuart Duff's excellent through pass sent Darren Mackie clear on goal but Falkirk keeper Dani Mallo, making his home debut, repelled the striker's forceful shot.
From the resulting corner, Mulgrew found Severin but Mackie, almost standing on the goal-line, blocked his team-mate's net-bound effort.
With nine minutes remaining to the interval, Higdon arrived just a fraction too late as he attempted to nod in Arfield's cross from the right.
Lovell then headed over from Neil McCann's cross as Falkirk ended the half the stronger of the two teams.
Falkirk opened the second-half in determined mood but could have found themselves behind before taking the lead in the 55th minute.
Severin had a header from another Mulgrew set-piece held by Mallo before play swept to the other end for Higdon to drive his side in front.
Lovell fed his strike partner in the inside-left channel and the Englishman rifled his shot into the top corner from the edge of the area.
Aberdeen manager Jimmy Calderwood responded by sending on Sone Aluko, Chris Maguire and Tommy Wright but it was Falkirk who came closest to a goal in the game's finale.
Lovell should have put the game beyond doubt with two minutes remaining as he raced clear on to Scott Arfield's pass but his lob over Langfield fell agonisingly on the wrong side of the post.