The young Tangerines' slipped to defeat at Tannadice in a closely fought encounter.
Early on Falkirk had the better of things and twice home keeper Marc McCallum was called into action.
After six minutes, he was at full stretch to keep out Conor Hogg's curler from the edge of the box.
And midway through the opening half, he more comfortably held on to a Michael Martin effort.
But before the interval, only two terrific saves by the visiting keeper prevented the Tangerines going ahead.
A great run by debutant and former real Madrid youth striker Rafa Malaga ended with a raging drive with Bowman at full stretch to tip over.
Then on the stroke of half-time, Chris McLaughlin whipped in a free-kick from which Aidan Connolly's header was acrobatically palmed over by the Bairns' keeper.
Just before the hour mark, Botti Blabbi fluffed his lines right in front of goal, his tame effort easily collected by McCallum.
On 66 minutes, however, Falkirk took the lead.
Scott Shepherd cut in from the right before firing a low shot from 10 yards inside the near post.
But apart from Jamie Montgomery hitting the post, the tiring home side didn't look like salvaging a point.
Dundee United: McCallum, Gilmour, McLaughlin, S Smith,
Ballantyne, Harwood, B Smith (Coote 72), Montgomery, Malaga, Fraser, Connolly.
Substitutes not used: McGovern, Allan, H Souttar.