Lee Wilkie's header on the hour-mark was enough to send Dundee United through to the quarter-finals of the CIS Insurance Cup.
Patrick Cregg missed a penalty for the hosts after 52 minutes when he was felled by Prince Buaben - and United made them pay for their profligacy.
Wilkie headed home Barry Robson's corner and Falkirk pressed for an equaliser without success.
David Robertson struck the post for United and the visitors held on.
Goalscoring opportunities were few and far between in a low-key first half at the Falkirk Stadium.
John Hughes introduced Russell Latapy after the break in an attempt to give the Bairns a cutting edge.
Latapy made an instant impact when played in Cregg, who was brought down by Buaben in the box.
Cregg's spot kick struck the crossbar before going over.
On the hour mark the Bairns found themselves a goal behind from Wilkie's header.
Robson's in-swinging corner from the right was met by Wilkie inside the six-yard box and he glanced the ball in to the net.
Falkirk: Krul, Holden, Scobbie, Milne, Barr, Cregg, Arfield, Thomson (Latapy 48), Riera (Moutinho 67), Barrett (Finnigan 70), Higdon. Subs Not Used: Olejnik, Aafjes.
Booked: Higdon, Riera, Scobbie, Cregg.
Dundee Utd: Szamotulski, Dillon, Dods, Wilkie, Flood, Bauben, Kerr, Gomis (David Robertson 90), Robson, Jordan Robertson, Hunt. Subs Not Used: McLean, Robb, Cameron, Kenneth.
Booked: Robson, Bauben, Jordan Robertson.
Goals: Wilkie 60.
Att: 2,804
Ref: C Thomson
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