The first half was devoid of excitement and the second was equally dull until the visitors took the lead when Shane Long turned in James Ward-Prowse's cross with 20 minutes left.
Swansea had a loud appeal for a penalty turned down when Alberto Paloschi tumbled in the area.
Southampton remained relatively untroubled as they completed a double over Swansea and extended their unbeaten league run to six games to move into sixth place.
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(Reporting by Martyn Herman)
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