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.
5. Leandro Trossard- 7
Was a driving force for Brighton’s attack. Found space well down the left hand side for Brighton’s second, sliding the ball through the defence, which, in an effort to prevent it from reaching Welbeck, Salisu turned into his own net.
6. Marc Cucurella- 6
A mixed game for the left back. Flew forwards and put the cross in which caused mayhem in the Southampton defence, eventually resulting in the Brighton opener. Gave away a couple of dangerous free kicks on the edge of the area, one of which resulted in Ward-Prowse inevitably firing into the bottom corner. Performed well when moved to centre back
7. Enock Mwepu- 5
Not the midfielder’s finest game. Was unable to wrestle control of the game in the middle of the park and was brought off after an hour.
8. Moises Caicedo- 7
Battled well in midfield, throwing himself into challenges, and showed good composure when on the ball. Quick feet helped him when pressed by Southampton and overall had a good game.