Albion are just 45 minutes away from Europa League qualification.
Evan Ferguson scored both goals as Brighton went in at the break 2-0 up.
He smashed the first past and underneath the body of Alex McCarthy, the Saints keeper.
The second was the result of a wonderful Kaoru Mitoma run and cross.
The young Irishman side-footed the ball home.
Southampton have had chances through Theo Walcott but so far they have failed to convert them.
Mitoma also hit the post after intercepting Walker Peters playing out of the back.
Albion will officially achieve greatness if the score remains the same or better over the next 45 minutes.