Tam McManus fired home the visitors's second before the interval.
Gordon Smith headed a goal back for the hosts and Falkirk's Stephen Kingsley was sent off for a professional foul on Michael Doyle but the Bairns held on.
Stirling: Reidford, Welsh, Doyle, Allison, Flood (Stirling 85), McHale, Aitken, Robertson, Borris (Brass 82), Smith, Brighton (Kane 82). Subs Not Used: Christie, Ashe.
Booked: Smith, Robertson.
Goals: Smith 53.
Falkirk: Olejnik, Duffie (Finnigan 57), McLean (Kingsley 86), Scobbie, Twaddle, Stewart, Millar, Murdoch (Mitchell 46), Higginbotham, McManus, Flynn. Subs Not Used: Barclay, Jay Fulton.
Sent Off: Kingsley (88). Booked: Murdoch, Duffie, Millar, Finnigan.
Goals: Millar 37 pen, McManus 41.
Att: 1,288
Ref: Stevie O'Reilly
Source: BBC Sport
Source: BBC Sport