Sadio Mane marked his return to the Southampton starting XI with a superb performance at Selhurst Park on Boxing Day, as he opened the scoring with an excellent early goal, before turning provider for Ryan Bertrand to double the visitors' lead straight after half-time.
Defender Toby Alderweireld, on loan from Atletico Madrid, then opened his Premier League account with a towering header shortly after to seal all three points for Ronald Koeman's men, despite a late Scott Dann consolation for the hosts.
Southampton showed some of the swagger and quality that led to them rising as high as second in the table before a slump of a draw and four losses from five games.
However, they got back on track with a 3-0 win over Everton last time out, and can now look forward to Sunday's visit of table-topping Chelsea with confidence.
Palace, meanwhile, have now won just one of their last 12 Premier League fixtures and slip into the relegation zone courtesy of Hull City's win at Sunderland.
Out-of-form Palace looked set for another difficult afternoon right from the off as Koeman's team began on the front foot.
Mane latched on to James Ward-Prowse's first-time pass to get in behind the home defence, before coolly rounding Speroni and applying the finish.
Forster then made a comfortable save from Palace skipper Mile Jedinak's free-kick, before Frazier Campbell rattled the bar having contentiously been given offside.
After some good work down the right by Mane, he produced a driven cross that eventually found Bertrand on the edge of the box, and the full-back confidently lashed home.
And their lead was extended further just six minutes later, when a simple clipped corner was met by Alderweireld, who rose highest to power home a header.
To their credit, Palace kept fighting and got a goal back through Dann in the 86th minute, as the defender nodded in Jedinak's corner.
But it was too little, too late for Neil Warnock's men, who look set to be involved in a relegation dogfight.
