It must have been a match which frustrated Craig Levein as his troops contrived to miss so many chances, that he would have almost lost count.
With barely 90 seconds on the clock and a strong wind behind them, the Terrors were to set the tone of the half and they really should have grabbed the lead when a wonderful cross on the outside of the boot from Noel Hunt was met by the head of Mark De Vries, but shaded past the outside of the post.
The Bairns' only real threat of the half was when Pedro Moutinho was a shade offside as he rounded Lukasz Zaluska to net in the seventh minute.
In-form Hunt was again denied in the 15th minute when a wonderful 18-yard strike was brilliantly tipped around the post by the acrobatic Robert Olejnik.
And the pressure continued on the visitors goal when a neat four-man move in the 21st minute ended with Prince Buaben's fierce overhead kick being well blocked on the line by Kevin McBride.
This was immediately followed by a Darren Dods cutback from Danny Swanson's corner which Christian Kalvenes looping header came off the bar
With United in complete command, there was a claim for a goal in the Tangerine support on the 29th minute when a De Vries header appeared to be over the line, but the Austrian keeper did well to hold his position despite pressure from Hunt and the whole ball was adjudged not to have crossed the line.
Six minutes later a great turn and shot from De Vries went past the wrong side of the post. And just before the break a fierce Buaben shot was well saved by the keeper.
The Bairns introduced Russell Latapy but the general direction of play continued to be towards the visitors goal, as United continued to create the chances.
A mazy 30-yard run from De Vries in the 55th minute ending with a shot just wide after it looked as if he had done all the hard work. And the big striker came so close four minutes later when he bulldozed a shot again narrowly wide.
It took Falkirk 62 minutes to create their only attempt on goal with a piece of Latapy magic conjuring up some space, but his curling 12-yard shot drifted wide.
But United just kept on missing chances. A Willo Flood corner was headed down by Lee Wilkie and volleyed over from only three yards by Kalvenes.
And, from United's 10th corner, a fantastic stop from Olejnik prevented Wilkie's volley from hitting the net and giving the Terrors a deserved late winner.