Two first-half goals put the home side in command against a strangely lacklustre Falkirk.
The visitors were first to show after four minutes when Arnau Riera picked up a loose ball in midfield and threaded it wide to Pedro Moutinho, whose driven cross was spilled by Jamie Langfield only for Scott Severin to clear with Graham Barrett ready to pounce.
Falkirk continued to press with the home side very much on the back foot and poor in possession.
The Dons took an unlikely lead on 15 minutes when Lee Miller was needlessly fouled 20 yards out by Darren Barr.
From the resultant free-kick, Jamie Smith curled a brilliant effort over the wall and into the postage stamp and opened the scoring.
Aberdeen had taken confidence from the lead and on 23 minutes an excellent cross-ball into the area from Jackie McNamara found the head of Steve Lovell, whose downward effort brought an excellent stop from Tim Krul.
Minutes later some fantastic play out of defence from the Dons almost brought a classic second goal.
The ball was moved swiftly from Jeffrey de Visscher to Barry Nicholson, who slid it wide to Derek Young.
He in turn rolled the ball into the feet of Lovell, who held it up long enough for the midfielder to advance on to the return pass before smashing a thunderous effort which crashed off the crossbar.
With the home side now in full flight Miller tried an audacious effort wide on the right from 35 yards which flew off the far post with the keeper again beaten.
Almost on half-time, Aberdeen added a deserved second goal.
Miller's smart turn and shot was only parried by Krul and the ball broke to de Visscher, whose low effort took a slight deflection before finding the back of the net.
The home side were not to be denied as they extended their lead on 56 minutes.
Jamie Smith was the quickest to react to a loose ball inside the area to smash the ball home from eight yards.
The visitors were handed a lifeline on 61 minutes when Alexander Diamond was penalised for handball.
Barnett netted the resultant penalty after Langfield had blocked his first effort.
Aberdeen should have put the game beyond the visitors on 71 minutes when Miller was brought crashing to the ground by Krul as he raced on to an intelligent through ball from de Visscher.
However, Dons skipper Severin's penalty kick was too close to the keeper who parried the ball wide.