Two composed finishes from Ryan McCord earned the Tannadice second-string the three points at Prestonfield, Linlithgow this afternoon.
It was a hard fought encounter of relatively few chances with United getting their goals at just the right times.
United threatened first with a Danny Swanson inspired move up the left, resulting in Olejnik blocking David Robertson's close-range effort.
Though United had a lot of possession in the early stages, it was without testing the Bairns' keeper.
However, the Bairns ought to have gone in front on the half hour mark. John Stewart came through two weak challenges and although Michael McGovern did well to parry his powerful drive from 12 yards, the striker blazed the rebound over the bar when he should have netted.
The home side were left rueing that miss eight minutes later when Danny Swanson cut the ball back after a good run to the by-line and though it was cleared, the ball fell to McCord who intelligently steered his side-footed effort into the net from 14-yards.
The hosts did, however, start the second half brightly, but United soon regained their grip on proceedings again
However, with the game slipping away from the home side, Mark Stewart cracked in a shot that McGovern confidently pushed away. At the other end, Olejnik was equally impressive with a great one-handed save to deny Robertson in 76 minutes.
But four minutes later, United did get a second to seal the points.
The architect was Prince Buaben who came through challenges before plying the ball to Andis Shala and he played McCord in to slip the ball under the advancing keeper from 10 yards.
United had no trouble running down the clock, and indeed, had the best chance of the latter stages with McCord going very close to completing his hat-trick.
Falkirk: Olejnik, Murdoch, McCaffrey (McLeish 75), Stallard, Staunton, Riera, Stewart J, Cregg, Stewart M, Lynch (Sludden 85), Moffat. Subs not used: Andrews, McLean P, Schultz-Eklund.
Dundee United: McGovern, Watson, Kenneth, Pope, Grainger, Cameron, Buaben, McCord, Swanson, D Robertson, Shala. Subs not used: Grant, Andreoni, Milligan, Dow.