The game got off to a blistering start when Jamie Smith put the visitors ahead after only three minutes.
A long clearance by Jamie Langfield was knocked down by Steve Lovell who combined well with Barry Nicholson. He got the break of the ball and shot straight at Tim Krul who saved well, only for the rebound to be tucked away by Jamie Smith.
Aberdeen's lead did not last long though as Falkirk drew level two minutes later. Pedro Moutinho's corner found Darren Barr at the near post and he rose to head home off the underside of the bar past the despairing Langfield.
However, Aberdeen were back in front in the ninth minute. Lee Miller was not picked up after a throw-in on the left. He cut inside and set up Lovell who got the deftest of touches to steer the ball past Krul.
After the excitement of the opening ten minutes there was only a half-chance apiece for the rest of the first period.
The first of these fell to Scott Arfield on 18 minutes. The ball broke to him 18 yards out but his low shot was saved well by Langfield.
Miller - a constant nuisance to the Bairns defence - perhaps should have played in Nicholson but instead shot into the side-netting on 20 minutes.
The second period started like the first had ended with plenty of endeavour but little in the way of goalmouth chances.
The first chance of the half came on 60 minutes when Alexander Diamond's header from Nicholson's corner was deflected just wide via Lovell's head.
Two minutes later a poor pass by Thomas Scobbie was cut out by Nicholson who shot ambitiously from halfway with Krul out of his goal, but his effort sailed over the bar.
Falkirk brought on talisman Russell Latapy on 69 minutes and equalised five minutes later. Carl Finnigan beat Scott Severin and got to the byline before crossing for Arnau Riera to send a diving header into the net.
Now that they were level, the home side really took the game to Aberdeen forcing a string of corners but with no end product.
The last chance of the game fell to the visitors, but Richard Foster's left-foot shot was deflected wide to ensure a replay.