In a game of two halves the Dons held the upper hand during the first 45 minutes to into the interval two goals ahead.
However, John Hughes's team-talk at half-time had the desired effect as the visitors pushed the Dons back during the second period and can consider themselves a little bit unlucky not to get at least a share of the spoils.
Aberdeen had an early let-off when Anthony Stokes played Alan Gow in behind Michael Hart, but from a tight angle his crisp left-foot shot beat Jamie Langfield but ricocheted off the post.
At the other end, clever inter-play between Lee Miller, Gary Dempsey and Barry Nicholson, on six minutes, saw Darren Mackie get on the end of the latter's pass, however, under pressure from Kenny Milne his effort went well wide.
Minutes later, a forceful run by Richard Foster saw him drive through the midfield, taking him away from Vitor Santos, before smashing in a low-grounder from the edge of the area, the ball flashing just the wrong side of the upright.
A quickly-taken free-kick on 17 minutes by Dempsey brought the opening goal. With the Falkirk rearguard napping, Mackie was on to the chipped ball into the area and deftly knocked the ball over the advancing keeper and into the net.
On 23 minutes, superb play between Gow and Stokes saw the on-loan hitman screw his right-foot shot just wide as the visitors pressed for an immediate equaliser.
Falkirk ought to have been back on terms on 33 minutes when a howler of a back-pass by Hart was seized upon by Gow, he cleverly pulled the ball back to Stokes, who completely mistimed his effort with the goal at his mercy.
On 42 minutes, Hart's long ball into the visitors area was chested down by Miller into the path of Nicholson, however, the midfielder's snap shot, from 20 yards, was way off-target.
With the visitors coming more into the game Aberdeen scored a very incisive second goal as the game edged towards half-time. Mackie played the ball through midfield to Chris Clark, who feigned to go wide before dragging the ball on to his right foot and from 25 yards out planted a sublime effort into the corner of the net.
On 47 minutes slick play from Jamie Smith took him away from Jack Ross as he drove at the visitors' centre-backs, before picking out Miller. The big striker cleverly turned Milne before lobbing the ball over Scott Higgins, only for the keeper to get the merest of touches, before gathering at the second attempt.
Smith was again prominent minutes later, sweeping in a great cross from the left, which saw Mackie clip the ball just over the crossbar.
On 55 minutes, Gow swept past several Dons defenders before firing in a left-foot effort, which looked to be heading into the top corner of the net, only an acrobatic twist and save by Langfield, pushing the ball over the bar, kept the visitors at bay.
Falkirk deservedly hauled themselves back into the game on 69 minutes, when, with the Dons defence backing off, Gow advanced to the edge of the area, where he swerved a unstoppable effort low into the net past Langfield.
From then until the end of the game the Bairns pushed men forward at every opportunity, but a resilient Dons rearguard held out to just about deserve to take all three points.