It was Brighton who took the lead in the first half after a shot from Veatriki Sarri led to an uncharacteristic error and own goal from England goalkeeper Mary Earps.
Straight after half-time, United came out fighting with Leah Galton finding the back of the net just minutes later.
The Reds went ahead through Alessia Russo with 20 minutes left but Brighton levelled things up once again when Danielle Carter capitalised on a Millie Turner error.
It took Marc Skinner’s side until 89 minutes to score the desicive goal with substitute Rachel Williams being the one to book the team a deserved place at Wembley.