The first opportunity of the game came after five minutes when Scott Severin narrowly headed a Jamie Smith free-kick just over the cross bar.
The home side had a scare after 10 minutes when Daniel McBreen timed his run brilliantly to ghost between the Dons' centre backs and advance on goal, only a block by Jamie Langfield stopping the big striker from opening the scoring.
Falkirk continued to hold the upper hand and again came close after 20 minutes. Pedro Moutinho skipped past Kevin McNaughton before sweeping in a great cross which was prodded goalward by McBreen only for Langfield to somehow turn the effort away at the expense of a corner.
Only a last-ditch clearance by Falkirk's Kenny Milne stopped Steve Lovell scoring after 24 minutes. However, this only delayed Aberdeen taking the lead minutes later. Danny Griffin chipped the ball into the area where slack defending by the visitors defence allowed Jamie Smith a sight of goal, and the diminutive striker smashed the ball home from 10 yards for his ninth goal of the season.
Enterprising play from Chris Clark after 37 minutes saw him drift pass two Falkirk defenders and, seeing Alan Ferguson off his line, he attempted a clever chip which drifted just the wrong side of the post.
Moutinho looked lively during the early exchanges of the second half, firing narrowly over from 25 yards having created a chance for himself out of nothing.
Superb individual skill by Falkirk youngster Patrick Cregg, saw him beat two Dons defenders to advance inside the area only to be stopped in his tracks by Alexander Diamond.
The visitors swarmed forward and deserved an equaliser when a Kenny Milne knock-down found Andy Lawrie inside the six yard box. He swivelled to fire in what he must have thought was a vital goal only for his effort to be charged away acrobatically by Langfield.
The home keeper Langfield again saved his side after 78 minutes when Alan Gow turned away from his marker before driving in a great effort which Dons goal keeper did we to turn roud the post.