Falkirk were keen to rewrite history, not having beaten Aberdeen in any competition since 1994, with the last win at Pittodrie for the Bairns coming 50 years ago.
The visitors were first to press, with Aberdeen goalkeeper Jamie Langfield fumbling the ball from Graham Barrett's early cross, which the Dons defence finally cleared.
The Dons roared back into the game and Smith opened the scoring with a glorious free-kick which he curled round the wall into the top left-hand corner of the goal.
Falkirk keeper Tim Krul was called into action when Steve Lovell met Jackie MacNamara's cross, but the on-loan Dutchman was equal to the effort.
Derek Young rattled the crossbar with a powerful effort from the angle of the box after a lovely one-two with Steve Lovell as Aberdeen continued to dominate.
Lee Miller then hit the post with another driven effort, with Krul totally beaten, as the Dons turned the screw.
The home side had totally dominated the opening half, and it was no surprise when Jeffrey DeVisscher doubled the Dons lead just before the break.
Krul saved the initial shot from Lee Miller, but De Visscher was on hand to fire in the rebound, his second goal for the club.
Lovell again went close after the break following fine work on the wing from De Visscher, as Aberdeen continued to control the match, but Krul was able to save the striker's effort.
The game was as good as over when Smith scored his second of the night, tucking the ball home at the back post after Kenny Milne failed to block the ball across the box.
Falkirk were handed a lifeline from the penalty spot after the referee adjudged Zander Diamond to have handled the ball in the box.
Graham Barrett saw Langfield save his spot kick, but the striker was alert enough to follow up and lash the ball into the roof of the net.
Aberdeen were then handed a spot-kick of their own, but Severin's effort was saved by Krul and the Falkirk defence cleared the ball, with Krul injuring himself in the process.
Robert Olejnik, on for Krul, did well to save from another Smith free-kick as the home side kept up the pressure late in the game.
Aberdeen: Langfield, McNamara (Daniel Smith 68), Diamond, Severin, Considine, Young, Nicholson, De Visscher (Jonathan Smith 90), Jamie Smith, Lovell (Maguire 78), Miller. Subs Not Used: Soutar, Aluko.
Booked: Young.
Goals: Jamie Smith 19, De Visscher 43, Jamie Smith 55.
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