In her first match as Seagulls manager, Melissa Phillips watched her new side take a shock lead in the first half when Mary Earps fumbled Veatriki Sarri’s cross into her own net for an embarrassing own goal.
Brighton’s half-time lead was extinguished within a minute of the restart, as Leah Galton finished from close range to bring the hosts level, and soon Marc Skinner’s interval team talk was looking a masterstroke when Alessia Russo fired them ahead with 20 minutes remaining.
But Brighton showed again they may be made of sterner stuff following Phillips’ appointment and refused to roll over, equalising through Danielle Carter after she had harried Millie Turner into an underhit back pass which she coolly slotted home.
There would still be heartbreak for the visiting Seagulls eventually though, still dreaming of a first FA Cup final themselves, when Williams was threaded through by Katie Zelem and slotted in an all-important winner a minute from time to send United to Wembley.