Melkamu Frauendorf netted an opener within 28 seconds of last weekend's clash at the Academy kicking off, but the Blues levelled from the penalty spot in stoppage time.
Mateusz Musialowski subsequently slotted in an excellent finish, though, to secure a memorable victory as Reds legends Sir Kenny Dalglish and John Barnes watched on.
Bridge-Wilkinson's charges now turn their attentions to Saturday's home meeting with Manchester United in the U18 Premier League North.
Liverpool are currently top of the division on goals scored, level on points with United and Manchester City, who each have two games in hand.