Kayleigh Green fired in a penalty and a thumping header in each half either side of Lea Le Garrec’s rocket before the break.
Blues manager Marta Tejedor made three changes from the 2-1 defeat at Manchester City in the FA Women’s Continental League Cup.
Injured trio Lucy Staniforth, Rachel Williams and Sarah Mayling were replaced by Connie Scofield, Claudia Walker and Academy prospect and first team debutant Freya Gregory.
Brianna Visalli donned the captain's armband with regular skipper Kerys Harrop also sidelined.
The Seagulls saw a fair amount of the ball early on without making much impression until referee Helen Conley pointed to the spot in the 11th minute.
A quick ball over the top played ex-Blues frontrunner Ellie Brazil in behind Rebecca Holloway with Harriet Scott sliding in to concede the penalty.
It took four minutes for Brazil, who would later be replaced through injury, to receive treatment but Green made no mistake with a firm finish high to Hannah Hampton’s left.
That put a spring in Brighton steps with Le Garrec firing over and a far-post scramble from Dani Bowman’s high cross forcing Hampton to push away.
Blues kept trying to find pockets of space when in possession and had a great chance to level in the 28th minute, Abbi Grant lifting the incisive through ball over Megan Walsh only for it to drop narrowly wide of the far post.
Grant was almost in again minutes later when Kirsty Barton’s clearance was more up than out but a kind bounce allowed the home skipper to recover.
Fliss Gibbons had a free header at the far post which Hampton saved and while Emily Simpkins nodded in the loose ball the offside flag went up.
A cutting Brighton move saw Brazil's replacement Matilde Lundorf and Green combine to find Le Garrec on the right to cross for Simpkins but her point-blank header was pushed onto the top of the bar by Hampton.
That close call proved a signal of what was to come, though, with Le Garrec pouncing on Walker’s pass inside to unleash a dipping, rasping finish off the underside of the crossbar.
The second-half saw little goalmouth action with Blues managing to get up the pitch more only to hit a stubborn Seagulls backline.
Good pressing from Scofield led to a loose pass being seized upon by Visalli whose swinging shot from just outside left corner of the box was blocked by a hand right on the edge of the area.
Any hope of a comeback was dealt a killer blow 19 minutes from time.
A delightful Le Garrec corner was crying out to be converted and Green obliged, crashing in an unstoppable header from no more than six yards.
Gregory succumbed to a knee injury in an awkward fall and was replaced by fellow Academy player Lily Simkin and the young full-back fared well, swinging in a cross to the far post with eight minutes to go which Barton found awkward to deal with.
That was a bit too close for comfort for the hosts but there was to be no Blues breakthrough.
Brighton: Walsh, Barton, F Whelan, Le Tissier, Gibbons, Brazil (Lundorf, 20), Simpkins, Bowman (c) (Nilden, 79), A Whelan, Green, Le Garrec.
Unused subs: Natkiel, Kerkdijk, Williams, Bance, Harris (gk).
Goals: Green 15 (pen), 71, Le Garrec 44.
Blues: Hampton, Arthur, Scottt, Holloway, Jordan, Gregory (Simkin, 62), Whipp, Visalli (c), Grant, Scofield, Walker.
Unused subs: Jones, Rabjohn, Brooks (gk).
Referee: Helen Conley.