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.
21. James Ward-Prowse-9
Never in doubt he would find the back of the net from a free-kick 25-yards out before levelling the score with a bullet from the edge of the box. Controlled the game in the second half. The Saints’ saviour.
22. Oriol Romeu-7
Let off massively after losing possession terribly on the edge of his box and then bamboozled by Trossard’s skill as somehow the ball wasn’t turned home at 1-0. Intercepted the ball for Ward-Prowse’s second before backheeling into his path for the assist. Broke play up well and much improved in second half.
23. Nathan Tella-7
Bright link up with Walker-Peters down the left involving good touches and interchanges. Did well to win a foul against Cucurella which Ward-Prowse scored from. One of the visitors most improved players in the second half before he was subbed with a knock.
24. Che Adams-7
Agonisingly close to poking home the leveller at 1-0 but couldn’t stretch far enough. Played well with his back to goal with good one touch play in the second half as his side moved it around more fluidly.