Falkirk had to rely as much on goalkeeper Mark Howard for the points as United will feel aggrieved to take nothing from a game they dominated.
Howard had to look sharp after only four minutes to race from his line to block a shot from Collin Samuel before Grant Brebner swiped a shot carelessly wide.
Howard had to earn his corn and did well again to tip a Brebner effort over his crossbar after he was left exposed again when his defence failed to cut out a Samuel cross.
From the resultant corner, a head flick from Garry Kenneth beat Howard but Patrick Cregg was on the line to head the ball clear.
Falkirk took the lead against the run of play after 23 minutes. Cregg looked to have lost his chance when he chose not to shoot at the edge of the box but he played the ball to Jack Ross who rifled in a low right-foot shot from the edge of the area.
But United still held the upper hand and Howard managed to save a fiercely-struck shot from Samuel.
Falkirk threatened again on the break when Alan Gow sprinted clear of the United defence, but Craig Samson managed to get a hand to it to send the ball spinning for a corner.
Gow carved out another chance for himself midway through the second half after robbing Kenneth, but his 20-yard effort curled over.
But it was United who were again guilty of wasting an opportunity when David Fernandez shot straight at Howard from 12 yards before Ross managed to block a shot from Stuart Duff on the line.
Howard saved his best stop until late in the game when he leapt to push a Fernandez long-range effort over his crossbar as it was clear it was not going to be United's day.