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.
13. Solly March- 7
Was positive on the ball and looked a threat having come on. Took on players down the right hand side and delivered in a few dangerous looking crosses.
14. Jeremy Sarmiento- 6
Was really unable to affect the game in the little time he had on the pitch, having come on in the 85th minute.
15. Fraser Forster-5
Dealt with the ball across the box terribly for the opening goal. Made a comfortable save at the near post to deny Welbeck making it two. Kept the score at 1-0 with a great reaction save but couldn’t do anything for the eventual second.
16. Valentino Livramento-7
Deflected effort struck the post from 25-yards, was neat in possession and defensively sound. Unfortunately forced off after half hour with a serious injury that looked pretty innocuous.