Brighton made a blistering start and were ahead inside 76 seconds. Saints goalkeeper Fraser Forster failed to deal with Marc Cucurella’s low cross from the left and Danny Welbeck was on hand to poke into the empty net.
Southampton almost levelled when Livramento’s deflected effort struck the left post, with Adams narrowly unable to convert the rebound.
Brighton then had an effort disallowed for offside after Maupay headed home following a corner.
Southampton full-back Livramento was stretchered off in the 36th minute.
The England Under-21 international, who was sidelined by a knee injury earlier this season, stayed down after twisting awkwardly as he attempted to challenge Enock Mwepu and was replaced by Romain Perraud.
Brighton doubled their advantage in the 44th minute.
Saints defender Salisu diverted the ball into his own goal via the left post after attempting to prevent a Trossard pass reaching Welbeck.
Southampton halved the deficit in the fourth minute of added time at the end of the first half thanks to a James Ward-Prowse free-kick.
Saints levelled in the 54th minute as Ward-Prowse claimed his second of the afternoon.
Oriol Romeu touched the ball back to his captain on the edge of Brighton’s box and Ward-Prowse drilled into the bottom left corner in front of the travelling fans.
Here'show they rated at the Amex Stadium. Sonny Turner with the Brighton ratings and Cameron Winstanley looks at Southampton.
1. Robert Sanchez- 6
Wasn’t given too much of a chance with both goals which were fired low and hard into the bottom corner. May be disappointed with the free-kick as it was struck his side of the goal. Made a great save from a Shane Long effort on the edge of the box, diving full stretch and managing to hold onto the ball.
2. Joel Veltman- 7
Defended well throughout. Made a great sliding challenge on Shane Long just as the striker was about to pull the trigger inside the area, was given offside but replays showed he wasn’t, so was a vital tackle to prevent a goal.
3. Lewis Dunk- 7
The Brighton captain was a commanding presence at the back for the Seagulls, and could do nothing to prevent both goals his side conceded. Was especially impressive aerially, heading away numerous long balls and crosses.
4. Adam Webster- 5
An otherwise solid game ruined by a really poor pass out from defence, which led directly to Southampton’s equaliser. Brought off after an hour.