The Eagles went behind early on when Tyler Dibling stabbed home for bottom-of-the-table Southampton against the run of play, but mounted a spirited response to turn the match on its head.
After a succession of chances, Trevoh Chalobah turned home Will Hughes' corner kick to equalise, before Ebere Eze's thunderbolt early in the second period saw the Eagles go again.
A scrappier second-half ensured as both teams sought a game-changing fourth goal of the match, but Palace defended stoutly and threatened to add to their lead, in the end making do with a 2-1 victory.
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