For long periods the visitors enjoyed the lion's share of possession but were woeful in the final third of the pitch.
Falkirk took full advantage with some clinical finishing, to condemn United to defeat in appalling conditions at the Falkirk Stadium.
The Bairns made light of the driving rain and icy wind to grab the lead with their first attack. United's defence went to sleep as Pedro Moutinho raced on to Darren Barr's long ball to slip a neat finish through the legs of Grzegorz Szamotulski
And Falkirk almost added to their lead when Barr beat the offside trap to fire a volley straight at Szamotulski.
But United came back strongly and Sean Dillon missed a great chance heading Barry Robson's corner over the bar from six yards.
And the visitors came even closer when Mark Kerr's 25-yarder rattled the crossbar, before Tim Krul was at full stretch to save Morgaro Gomis' long-range shot.
But Falkirk took full advantage of United's failure to score with a second goal three minutes from the interval.
Michael Higdon's low cut-back found Graham Barrett making a run to the near post to fire home and leave United with a mountain to climb.
However, Falkirk were streets ahead after the break and Moutinho came close with a cheeky effort from a tight angle.
It was all over after 65 minutes after a great Falkirk goal. Skipper Steve Thomson knocked the ball out wide to Barrett and his driven cross was perfect for Higdon to power home a header.
It could have been worse for United as the impressive Scott Arfield came close from distance before sending a low shot inches wide after a fine Falkirk move.
The signs are good for the Bairns after a shaky start to the season. They have turned the corner with two wins out of two and eight goals to boot.