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.
17. Mohammed Salisu-4
Made a hash of dealing with the opener, should’ve taken charge of the situation. Was lucky Maupay didn’t connect with a free header after he failed to pick him up in the first half. Very untidy in possession. Own goal capped off a disastrous first half, improved in second half under late pressure.
18. Jan Bednarek-7
Covered round from flick-ons well, wasn’t at fault for either goals. Much the stronger of his centre half pairing both in and out of possession. Denied Welbeck a chance to win the game in added time with a good headed clearance.
19. Kyle Walker-Peters-8
Looked dangerous when joining in attacks, always positive. Last ditch tackle denied Mwepu a one-on-one from close range which kept them in the game. Switched to right-back after Livramento’s injury. Thrashed over a wild attempt late on.
20. Nathan Redmond-6
Played a good ball into the channel which Long should’ve done better with early on. Didn’t have as much success against Cucurella as he the visitors enjoyed on the other wing. Cheaply lost the ball on the half-way line under no pressure which Maupay didn’t punish.