A breathless encounter saw the Seagulls take the lead after half an hour through Elisabeth Terland, after a slick passing move.
Marc Skinner's side forced our way back into the game with little over 10 minutes of the second half to go, courtesy of an excellent Ella Toone strike from the edge of the area.
Guro Bergsvand looked to give Brighton the win with her late headed goal, but Rachel Williams popped up even later for the Reds to snatch a point at the death.
FIRST HALF
Skinner’s side looked to hit the ground running immediately at Broadfield Stadium, coming close to opening the scoring inside the first minute of the game.