Palace were happy to contain and hit on the break, and they did just that in the 27th minute when Marouane Chamakh went clean through on Artur Boruc but fell too easily in the area and was booked by referee Martin Atkinson.
Southampton struck twice after the restart as Osvaldo scored his first goal for Southampton – and the Saints’ first from open play in the league this season – as he fired home left footed from just inside the area.
Rickie Lambert quickly added a second with a stunning free-kick to put distance between the teams after a disciplined first-half from Palace.
Palace were desperately lacking in quality and look to have a long, hard season ahead of them.
Southampton, who produced another solid defensive display, moved up to fourth place after this win.
PRE-MATCH: DAVIS IN FOR SAINTS, FOUR PALACE CHANGES - Southampton made one change from the side which won at Liverpool, with Steven Davis replacing Jay Rodriguez who dropped to the bench. Ian Holloway made four changes from the team which lost 2-0 at home to Swansea, with Joel Ward, Kagisho Dikgacoi, Jimmy Kebe and Dwight Gayle all coming in.
5’ – CHANCE: The ball breaks in the area for Morgan Schneiderlin who heads goalwards and it is cleared off the line by Joel Ward. Lucky escape for Palace.
22’ – CHANCE: Osvaldo finds Adam Lallana in the area who shows quick feet to play the ball back to Lambert and the England striker curls just over the bar.
27’ – PENALTY APPEAL REJECTED: Chamakh goes clean through on goal and goes down under a challenge from Artur Boruc. The Moroccan is booked for diving.
47’ – GOAL - Osvaldo opens his account for Southampton with an excellent low finish. Lallana finds him just inside the area, Osvaldo evades Kagisho Dikgacoi, and curls low into Julian Speroni's bottom right corner.
49’ – GOAL - Lambert produces a superb free-kick to double Southampton's advantage. Danny Gabbidon looked to be ducking in the wall, but Lambert won't care as he gives Speroni no chance with a curling free-kick that flies into the corner.
TALKING POINT: Marouane Chamakh produced the kind of dive that is becoming more and more prevalent in the game. Through one-on-one with Artur Boruc, the Moroccan preferred to go down than shoot and was rightly booked by Martin Atkinson as he was already on his way down before even coming into contact with the goalkeeper.
Crystal Palace looked a side desperately lacking in creativity and failed to register a shot on target in the entire game.
MAN OF THE MATCH
Dejan Lovren (Southampton): One of the reasons Palace looked so porous in attack was because Lovren and Jose Fonte defended impressively. Southampton have conceded just two goals in six games and it is in no small part down to the Croatian who has adapted seamlessly to English football.
SOUTHAMPTON: Boruc 6, Clyne 6, Fonte 8, Lovren 8, Shaw 7, Wanyama 7, Steven Davis 7, Schneiderlin 7, Lallana 7, Osvaldo 7, Lambert 7. Subs: Ward-Prowse 6, Ramirez N/A, Rodriguez 6.
CRYSTAL PALACE: Speroni 6, Ward 6, Mariappa 6, Gabbidon 7, Moxey 7, Dikgacoi 6, Jedinak 6, Bannan 6, Kebe 5, Gayle 5, Chamakh 5. Subs: Thomas 6, Jerome 6, Phillips N/A.