The Pars deservedly progressed to the fourth round of the Youth Cup, but only after finally overcoming the Tangerines' dogged resistance.
Little separated the teams in the first half. The Fifers had the better of the early exchanges but apart from United keeper Joe McGovern beating away a Ryan Williamson shot after 14 minutes, they rarely threatened.
Indeed, towards the interval, the Tannadice side started to dictate with home keeper Cammy Will saving from Mark Russell and Jamie Montgomery.
However, after the interval, the Fifers dictated and looked to have gone ahead when Lewis Martin finally beat McGovern, but the goal was disallowed for an earlier infringement midway through the half.
With 15 minutes left, Scott Mercer clipped the bar from a free-kick as the home side maintained their stranglehold.
And eight minutes from time they finally broke Tannadice resistance, Gavin Hamilton heading home a Mercer corner.
Then, with four minutes left, McGovern thwarted Lewis Marti, palming his pile-driver from just outside the area.
Dunfermline Ath:Will. Williamson. Drummond, Martin, O'Kane, Spence, Moore, Graham, Smith, Gray, McMillan.
Substitutes not used: Orru, Forrest, McClair, Thomas.
Dundee United: McGovern, Spark, Gilmour, Ballantyne, Harwood, Hendry, Connolly, Montgomery, M Russell, Fraser, McLaughlin (Tumilty (72).
Substitutes not used: Allardyce, Walls, Hornby.
Please note that the next United U20s League game is v Rangers at Tannadice. This game will be played on Wednesday 23 October with a 6pm kick off. Admission £3 and £1 - season ticket holders watch for free.