Neal Maupay put Albion in the lead on 17 minutes after good work from Glenn Murray.
Maupay wrong-footed Saints keeper Alex Macarthy and slid the ball home.
Solly March has looked lively for the Seagulls as had Murray, with both causing the Southampton defence problems.
A combination of Danny Ings and Albion’s Tariq Lamptey looked to have equalised for Saints but assistant referee Massey-Ellis raised her flag for offside and this was confirmed by VAR.
Some fans will be hoping Murray can get his second Premier League goal of the season and what could be his 105th in Albion colours.
Oriol Romeu was booked for Southampton after just seven minutes and walks a tightrope.
Albion fans will have been relieved to see Theo Walcott equalise for Everton to secure a draw against Aston Villa earlier this evening.