Sadio Mane scored the opening goal just before half-time, and Graziano Pelle extended the lead 15 minutes into the second-half having replaced Oriol Romeu at half-time.
Jason Puncheon responded against his old club with a terrific effort following a corner, but Ryan Bertrand restored the two-goal lead soon after with a well-taken penalty.
Steven Davis made sure of the win with a fierce drive from close-range.
Pardew makes changes to side with cup final in mind
Alan Pardew made five changes from last weekend's 2-1 victory against Stoke City. Wayne Hennessey, Scott Dann, Yohan Cabaye, Yannick Bolasie and Connor Wickham dropped out of the side and were replaced by Julian Speroni, Adrian Mariappa, Mile Jedinak, Jordon Mutch and Emmanuel Adebayor.
The Eagles' boss was also able to name youngsters Sullay Kaikai and Jake Gray on the bench, while Speroni equalled John Jackson's record of 388 appearances in the Palace goal.
Southampton dominate first half and head into break with the lead
Southampton - fighting for a European place - started the better of the two sides and enjoyed large spells of possession. Midfielder Victor Wanyama had their first meaningful effort when the ball fell his way on the edge of the box, but his side-footed effort flew high over Speroni's goal.
Dwight Gayle was lively for Palace following his match-winning double against Stoke, and had hs side's first chance when he managed to get to the ball before the Saints defenders and saw his shot well saved by Forster.
Ronald Koeman's side continued to threaten with Mane and Romeu both going close to giving their side the lead, but neither could beat Speroni.
Gayle remained the most threatening player in the Palace side and came close once again but similarly to his previous effort, Forster stood in his way.
Palace enjoyed their best spell of the half just after the 30-minute mark; Puncheon, Joel Ward and Pape Souare all had efforts from long-range but none tested the resilient Southampton goalkeeper.
Mane finally broke the deadlook two minutes before half-time when he capitalised on a mix-up in the Palace defence to squeeze the ball past Speroni.
Palace appeared to have next week's cup final on their minds during the game and seemed lethargic throughout the first-half, with the defending for the goal epitomising this.
Gayle had one final chance for Palace before the half drew to a close, but, once again, found Forster in his way from close range.
Kaikai introduced at half-time, but Palace woes worsen in second-half despite Puncheon goal
Mutch was replaced by Kaikai at half-time following an ineffective first-half performance - the latter made his Premier League debut. Graziano Pelle also replaced Romeu for Southampton as they changed formation in the second-half.
Southampton continued to threaten after the break and Shane Long had their first effort with a long-range drive which was blocked en route to goal.
Forster remained in superb form and was at his best to deny Kaikai a goal on his Premier League debut when he struck a volley goalwards.
The save turned out to be crucial as Southampton extended their lead just two minutes later when substitute Pelle headed home.
However, Puncheon halved the deficit against his old club soon after when a corner was cleared his way on the edge of the box and he thumped the ball past Forster - who had appeared to be unbeatable beforehand - and into the top corner to give his side hope.
The goal gave the Eagles a sense of belief and they were roared on by the travelling support at St. Mary's as Palace advanced forward to find an equaliser, which seemed out of reach just minutes before.
James McArthur then came close when he saw two shots blocked in quick succession following great work from Kaikai, who was having a magnificent influence on his top-flight debut.
Despite the flurry of Palace chances, Southampton secured the result and restored their two-goal lead when Mane won a penalty following a succession of challenges from Mariappa and Souare. The contact appeared to be made outside the box, but referee Michael Oliver had no hesitation in pointing to the spot. Bertrand was the player chosen to dispatch the kick and he did it in exquisite fashion, firing into Speroni's top corner.
McArthur was given a rest for the final 15 minutes as Pardew began to look ahead to next week's FA Cup final, and his replacement, Chung-yong Lee was likely to be playing his last game for the Eagles following his comments in the South Korean media.
Steven Davis added further insult to injury when he rifled home following a knock-down from Pelle, as Koeman's side eased their way to victory on the final day.
The result means little for Palace, who finish the season in poor fashion. But all attention will now turn to next week's FA Cup final against Manchester United.