Two goals in the space of four second-half minutes enabled Aberdeen to book their place in the quarter-finals of the Tennents Scottish Cup.
The Dons had to overcome both a physical Falkirk side and some appalling weather, with much of the game being played in blizzard conditions.
But in the end goals from David Zdrilic and Scott Booth were enough to dump the Bairns at their borrowed Ochilview stadium.
Aberdeen had made the better start to the game and former Falkirk player Steve Tosh forced goalkeeper Alan Ferguson into an acrobatic save with a fierce
long-range effort in the 21st minute.
Three minutes later, Booth found space in the box and chipped over the goalkeeper - but his effort also cleared the far post.
The home side, who famously thrashed Hearts in last years competition, gradually came into the game.
And Falkirk almost got lucky when former Rangers man Russell Latapy sent in a cross from the left and goalkeeper David Preece realised he had to tip it over.
Aberdeen survived a penalty shout when Davide Xausa went down under Russell Anderson's challenge.
The snowy conditions meant a yellow ball was sent on and when Tosh fowled Kieran McAnespie some 20 yards in front of the goal, the Falkirk midfielder forced Preece into a fine tip over when he took the free-kick himself.
Aberdeen suffered a set back just before half-time when Kevin McNaughton had to be stretchered off when he was hurt defending a corner.
Phillip McGuire replaced him at the back for the second half and Preece needed to make another stop from a close-range Xausa header from a corner.
Both the Canadian and McAnespie were taken off just before the hour-mark, with David Nicholls and former Nottingham Forrest Striker Jason Lee coming on.
A fine ball from Booth allowed Leigh Hinds to take the ball around the goalkeeper, but the angle was too tight and Craig McPherson was able to tidy up comfortably.
But then Aberdeen finally took a grip on the game which was to prove decisive after an hour's play.
Ferguson did well to parry a fierce long-ranger from Tosh and again got a touch when Aberdeen forwards converged on the loose ball which would have trickled behind the goal-line had Zdrilic not been alive to the situation and
turn it between the posts in the 61st minutes.
At the other end, Lee headed a great chance over after Latapy's cross from the left - and that miss was to prove costly when Booth made it 2-0 straight after
by turning in a low Chris Clark cross from close range.
Lee blasted another great chance over with Latapy again the man who had set it up - and the Falkirk fans new at that moment that the game was lost.
Teams
Falkirk Ferguson, Lawrie, Hughes, Sharp, McPherson, O'Neil,
MacKenzie, Latapy, McAnespie (Nicholls 57), Xausa (Lee 57),
Colquhoun.
Subs Not Used: Scally, McSween, Hill.
Booked: Hughes, Nicholls.
Aberdeen Preece, McNaughton (McGuire 46), Diamond, Anderson,
Morrison, Tosh, Heikkinen, Clark, Hinds, Booth (Prunty 84),
Zdrilic (Muirhead 74).
Subs Not Used: Esson, Sheerin.
Booked: Tosh.
Goals: Zdrilic 60, Booth 64.
Att: 4,747
Ref: K Clark (Scotland).