Nigel Adkins's side, unbeaten at home this season, dominated the first half and were rewarded with a goal just past the half-hour mark when Guly Do Prado gave the Saints the lead.
Steve De Ridder teased the Palace defence down the right before floating a cross in for Do Prado to convert with a towering header.
The second half was a more even contest, with the visitors finally testing Kelvin Davis but Glenn Murray's shot was saved comfortably by the Saints keeper.
The Saints secured the points ten minutes from time when Do Prado doubled his tally by converting from Frazier Richardson's pinpoint cross.
Southampton next face Bristol City at St Mary's while Crystal Palace travel to Millwall.