A late goal in the 83rd minute of the game was enough to give former Red and United boss Casey Stoney a win in her first outing as a manager.
Going into the tie, Liverpool FC Women manager Neil Redfearn fielded eight debutants while United had five ex-Reds in their starting XI.
Liverpool FC Women made a bright start and came close after two minutes.
A surging run down the right flank from Satara Murray saw her cross find Leighanne Robe at the back post, but the left-back fired just wide.
On 27 minutes only a fine last ditch challenge from ex-Red Amy Turner denied debutant Kirsty Linnett opening the scoring, then a cross from Murray was fired across the face of goal with nobody able to pounce.