Mark Stewart netted Falkirk's second in the 64th minute but Dundee quickly pulled a goal back through Gary Irvine, who converted Nicholas Riley's cross.
And Dundee's comeback was complete nine minutes from the end when Craig Forsyth finished from 12 yards.
Falkirk: Olejnik, Perry, Scobbie, McLean, Twaddle, Stewart, O'Brien, Millar, McManus, Compton (Murdoch 75), Finnigan. Subs Not Used: Barclay, Higginbotham, Moutinho, Wallace.
Booked: Scobbie, Finnigan.
Goals: McManus 27, Stewart 64.
Dundee: Douglas, Irvine, McKeown, Weston, Lockwood, Riley, O'Donnell, Harkins, Forsyth, Mcintosh (Rennie 85), Benedictis. Subs Not Used: Gibson, Bartlett, Tulleth, Webster.
Booked: Riley, Benedictis, Forsyth, Douglas.
Goals: Irvine 65, Forsyth 81.
Att: 4,099
Ref: William Collum
Source: BBC Sport
Source: BBC Sport