Danny Ings, on loan from Liverpool, scored his second goal of the season in the 47th minute to put the Saints ahead and they should have doubled their lead but Charlie Austin saw a penalty saved by Palace keeper Wayne Hennessey.
Saints had keeper Alex McCarthy, called up to the England squad this week, to thank for a series of fine saves including a brilliant late stop to keep out a close-range effort from Palace striker Christian Benteke.
With Roy Hodgson's side piling forward in search of an equaliser, Southampton struck on the break with Pierre-Emile Hojbjerg's finish making sure of the victory in stoppage time.
(Reporting by Simon Evans; editing by Clare Fallon)
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