The Frenchman capped a sizzling solo run to score from an acute angle to give his side their first away league win of the season. Top scorer Lee Barnard headed his eighth of the season to give Southend an eighth-minute lead following a cross by Simon Francis.
Veteran striker Nicky Forster levelled with a precision finish in a one-on-one situation with keeper Steve Mildenhall after 21 minutes but debutant Roy O'Donovan restored Southend's lead with a tap-in following an Adam Barrett knock down six minutes later.
Southend were punished for slack defending as Forster hauled Brighton level again with his sixth goal in five games - an unstoppable shot into the bottom corner six minutes before the break.
The Seagulls finished strongly and substitute Dean Cox was only just off target with a low shot before Laurent pounced to give Southend a hard-fought win.