Farid El Alagui scored the only goal as Falkirk edged past Dundee into the third round of the Ramsdens Cup.
Dundee could have taken the lead inside the first minute but Stephen O'Donnell fired Ryan Conroy's cross over the bar.
He was made to rue that miss just two minutes later when El Alagui slotted home Craig Sibbald's cross from close range.
El Alagui might have doubled his tally with 30 minutes remaining but slashed wide when well placed in the area.
Falkirk: McGovern, Duffie, Dods, Bennett, Scobbie, Jay Fulton, Murdoch, Mark Millar, Sibbald (Dale Fulton 64), Higginbotham, El Alagui. Subs Not Used: Bowman, Wallace, Graham, Brisbane.
Booked: Murdoch, El Alagui.
Goals: El Alagui 43.
Dundee: Douglas, Irvine, McKeown, Weston, Lockwood, Riley, McGregor (Rennie 76), O'Donnell, Conroy (Webster 76), Hyde, McCluskey. Subs Not Used: Gibson, Benedictis, Mcintosh.
Booked: O'Donnell, Conroy, Irvine.
Ref: Brian Winter