Two goals early in the second half from Dani Osvaldo and Rickie Lambert secured the three points for Saints, who moved in to the top four of the Barclays Premier League with the win.
After a first half of very few opportunities it was Osvaldo who grabbed his first goal for the club moments after the restart with a Lambert free-kick two minutes later proving enough to kill off Palace.
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Wednesday morning's weather for the east of the region
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More than 30 huts have been burgled along Herne Bay pier, in what seems to be a systematic attack