The win came courtesy of lightning strikes from Dani Osvaldo and Rickie Lambert inside four minutes of the start of the second half, with the latter's free-kick the 200th league goal of his career.
Much was expected of the pairing but this was the first time either had found the back of the net since Italy international Osvaldo joined from Roma on August 18, and their efforts secured a comfortable triumph over Palace.
The first half had offered very little, with the main talking point coming when Marouane Chamakh was adjudged to have dived when through on goal for the visitors.
But Southampton started the second half much brighter and caught Palace cold as Osvaldo and then Lambert both finished well to put the hosts in a commanding position.
Saints came close to opening the scoring after just six minutes as Morgan Scheiderlin pounced on a loose ball in the box and looped a header towards goal.
It beat the onrushing Julian Speroni but was cleared off the line by Joel Ward just as it looked as though Mauricio Pochettino's side were about to take an early lead.
Palace were playing on the counter-attack and almost caught Southampton out when Jimmy Kebe, making his first start for the Eagles, and Chamakh combined, with neither able to get a shot away on goal.
Lambert was the next Saints player to come close to breaking the deadlock after Adam Lallana rolled a ball to the England international which he curled just over the top of Speroni's goal.
The Palace goalkeeper was forced in to action moments later as he got down low to punch Lambert's driven free-kick away. Osvaldo then miscued from Lallana's free-kick across the penalty area as the hosts looked to take control of the game.
Source: PA
Source: PA