The Saints got off to a real flyer. While Shefki Kuqi so easily had put Palace in front after just five seconds, Nathan Dyer then responded by racing up field to gain Southampton a corner.
From Rudi Skacel in swinging pick, Jones climbed well to power his header leaving Gabor Kiraly rooted on his line.
Inspired by their first minute opener Southampton were the slicker side with Skacel in a menacing mood. Still James Scowcroft rattled the crossbar on ten minutes which turned out to be Palace's only real chance in the first 45 minutes.
Meanwhile, Dyer had a good chance blocked and Kiraly had to be on his toes to dive low to stop Rasiak from scoring from 15 yards out. And right on half-time Jones went so close to add into the scoring that shot over after good work from Dyer and Rasiak.
Within four minutes after the break Southampton caught Palace out once again. Michael Hughes made a mess of things just outside the penalty area and the ball dropped nicely to Skacel on the left touchline.
The Czech midfielder then crossed perfectly into the goalmouth for Rasiak to fire home with a first time half volley from ten yards out.
Palace defender Leon Cort then had to head off his line to prevent Dyer from scoring from 40 yards out after Kiraly was forced to leave his own penalty area.
Southampton with John Viafara outstanding were completely running the show. The Colombian midfielder saw too rasping shots saved by Kiraly and later Rasiak fired over.
For Palace striker Kuqi did little to impress and was substituted just before the hour. Substitute Dougie Freedman wasted Palace's best chance in the second half as he drilled his shot just wide from 16 yards out and by the end Southampton were deserved winners.