It was a game in which the visitors had dominated the first half, but turned on the brilliance of Grzegorz Szamotulski.
After a non-eventful opening, the visitors came close courtesy of United's Darren Dods, when in the eighth minute he headed the ball off the face of his own bar.
Six minutes later, however, the Tangerines came close when captain Barry Robson weaved past four players before hitting a right-foot shot which Tim Krul did well to hold.
After a strong penalty claim by United when Gerard Aafjes appeared to handle the ball, the Tangerines came close again when some excellent wing play by Noel Hunt and Sean Dillon ended with Robson firing over.
But the half belonged to Falkirk with Russell Latapy thundering in a low shot which was well blocked and from the resulting corner Darren Barr volleyed off the outside of the post.
Just before the break, they really should have taken the lead when Pedro Moutinho and Latapy played an excellent one-two with the former laying the ball into the path of Michael Higdon, who with three players screaming for the ball, elected to back-heel for Lee Wilkie to clear.
The game, however, turned on one particular shot when a blistering 20-yard piledriver from Barr was magnificently tipped onto the inside of the post by Szamotulski.
In relief, the Terrors charged forward and came very close twice from Wilkie in the six-yard box.
And they finally broke the deadlock in the 58th minute when a long ball from Dillon was flicked on by Jordan Robertson for Hunt to run on and hit the ball low from 12 yards under the diving Krul.
United found themselves up against it in the 69th minute when Morgaro Gomis was given two yellow cards in the space of three minutes.
But the Terrors had the last laugh when Robson curled in a 16-yard beauty six minutes from time to seal all three points.