After beating first-place Chelsea 2-1 on Saturday for a fourth straight win, Palace took the lead against Southampton through Christian Benteke in the 31st minute.
But Nathan Redmond equalised in the 45th, before Japan defender Maya Yoshida's tap-in put Southampton ahead in the 84th and James Ward-Prowse added a third for the home side a minute later.
Palace dropped to within three points of the relegation zone and has a tough eight-game run-in that includes matches against Arsenal, Liverpool, Tottenham, Manchester City and Manchester United.
Southampton climbed from 13th to ninth place.
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Southampton XI: Forster, Cedric, Stephens, Yoshida, McQueen, Davis, Romeu, Ward-Prowse, Tadic, Redmond, Long
Subs: Clasie, Rodriguez, Caceres, Hojbjerg, Pied, Sims, Hassen
Crystal Palace XI: Hennessey, Ward, Kelly, Sakho, Schlupp, Cabaye, Milivojevic, Townsend, Puncheon, Zaha, Christian Benteke
Subs: Speroni, Flamini, Lee, Fryers, KaiKai, Sako, Delaney
Referee: Roger East (Wiltshire)