The visitors started very brightly but when Jay Rodriguez let fly with a great volley he was unable to keep the ball down and it flew over Julian Speroni's goal.
In the tenth minute Speroni did well to keep Steven Davis' hooked effort out and, after a very dull period of play, Rodriguez saw his shock blocked on the half-hour mark after a rapid Saints counter-attack.
The visitors deservedly took the lead in the 37th minute when Rodriguez rolled the ball into an empty net from 20 yards out after capitalising on former Southampton star Jason Puncheon's poor defensive header on the halfway line.
Rickie Lambert almost doubled Saints' lead just before the break but his shot hit the outside of the post before the ball was eventually cleared by the Palace defence.
Palace did lots of huffing and puffing after the interval but they didn't have the quality to break down a well-organised Southampton defence.
Artur Boruc did have to be alert in the closing stages to claim the ball at the second attempt from substitute Cameron Jerome's header while Yannick Bolasie also forced the former Celtic goalkeeper to make a smart save, but Tony Pulis' side did not do enough to warrant taking any points from a dull encounter and are now only two points above the bottom three.