Falkirk avoided the bottom of the league by goal difference thanks to Ciaran McKenna's late header.
The former Celtic youth player rose to nod a pin-point Ian McShane free-kick in with eight minutes to go and maintained Falkirk's unbeaten start to the year.
HOW IT HAPPENED: MATCHDAY BLOG
It was a fairly even start with United just shading the opening exchanges and they almost took the lead in freak circumstances on five minutes when Jordan McGhee headed off his own crossbar, but Mark Connolly blazed the rebound well over.
The Bairns' best chance came when Deimantas Petravicius burst to the by-line on the half hour mark. The Lithuanian had the chance to play in Zak Rudden, but the on-loan Rangers man had strayed slightly offside, and the winger was right to carry on his run. But he elected to shoot rather than roll across goal, and blazed over from a tight angle.
Benjamin Siegrist didn't have to do much with it, but he was at full stretch five minutes later to tip over a McShane free-kick after Davis Keillor-Dunn was fouled on the edge of the area by Calum Butcher.
LEAGUE TABLE: SPFL Championship
With news in the first half filtering through of Alloa's lead against Queen of the South and Partick's two-goal advantage over Ross County the implications of which saw Falkirk drop to the bottom of the league despite holding United to a goalless first half.
It was uninspiring stuff though and made all the worse just after the break when Cammy Smith tapped in Jamie Robson's burst to the by-line.
That prompted Ray McKinnon to switch to a 4-4-2 with Aaron Jarvis introduced for his debut, but the tactical move only served to give United more room to operate.
The momentum was all with the away side and only good fortune for the Bairns kept the scoreline down.
There was misfortune for the Tannadice side though as Rachid Bouhenna, himself a first half replacement for the stretchered Frederic Frans, was carried off himself after a clash at a corner kick.
PLAYER PROFILE: Ciaran McKenna
The changes didn't interrupt the flow of the game much, which was all directed to Harry Burgoyne's goal and the keeper looked shaken by the constant attention around his area.
Ciaran McKenna did test Benjamin Siegriust with a good header at the other end after an accurate Ian McShane corner kick, but he would go one better with McKinnon's final roll of the dice.
Replacing Rudden with Nikolay Todorov prompted the Bairns support to rise to their feet in acclaim of another all action performance from the loan Ranger. And they barely had cause to sit down again with a frantic finish to the game.
Another United player hit the deck and prompted fury from the Falkirk fans, then at the re-start Paul Paton was cynically fouled. He roared. The fans roared, then they all did.
Falkirk went level with McShane finding McKenna who nodded into the net and sent the home end wild, and after a timid performance it was all to play for and play swung end to end for the remaining eight minutes.
In the end, Falkirk avoided the drop to the basement that had looked so likely just a few minutes earlier, with Partick Thistle's 4-2 defeat to Ross County sending the Firhill side bottom on goal difference, and Alloa defeating Queen of the South in Dumfries.