The game began brightly although it took 31 minutes for either side to create an opening.
It came when Lee Miller showed great skill on the touchline before sending Barry Nicholson clear down the right and his cross was only just missed by Chris Clark.
Four minutes later Scott Severin found Miller whose touch took the ball into the path of Clark and his right-foot shot was well saved low to his right by Tim Krul.
Falkirk's best chance of the first half came a minute before the break when a ball over the top found Carl Finnigan in acres of space but the Bairns star blazed his shot wide of the target.
The opening goal came in first-half stoppage time when Alexander Diamond's cross was handled inside the area by Darren Barr and the referee had no choice than to award a spot-kick.
Aberdeen captain Severin stepped up and sent his low right-foot shot into the corner of the net to put the Dons one up at the break.
Aberdeen centre-half Diamond almost gifted Falkirk an equaliser eight minutes after the re-start when he allowed himself to be robbed by Graham Barrett just inside his own half.
The player then ran forward to the edge of the area before crashing a shot just wide of the upright.
Aberdeen's Derek Young won a corner in the 65th minute and swung a dangerous cross towards the six-yard box which Jackie McNamara headed just wide of the far post.
Three minutes later Falkirk drew level after winning a free-kick on the left-hand side. Scott Arfield swung the ball across the six-yard line where it was headed out by Miller. However, it landed perfectly for Patrick Cregg who fired his low shot through a ruck of players and into the back of the net.
With ten minutes remaining Sone Aluko's cross-cum-shot nearly caught out Krul but the big keeper was able to touch the ball onto the post before it went to safety.
In the closing stages another Aluko cross was met at the near post by Miller's flying boot but his touch took it just wide of the goal.