Match ends, Crystal Palace 0, Southampton 2.
Southampton boss Mark Hughes said his players had shown a "real purpose" after they secured their first win of the Premier League season with victory at Crystal Palace.
Danny Ings, signed on loan from Liverpool in the summer, confidently netted his second goal of the campaign to put the visitors in front after being set up by Cedric Soares.
Substitute Charlie Austin, who scored the Saints' Carabao Cup winner against Brighton in midweek, had the chance to double the lead on 65 minutes but his weak penalty - after Aaron Wan-Bissaka's handball - was saved by Wayne Hennessey.
Pierre-Emile Hojbjerg added the second in stoppage time after the visitors, with two defeats and one point from their opening three matches, had to soak up concerted pressure in the closing stages.
"The last two weeks, since the Everton defeat, I've seen a real purpose to everything we have done in terms of application and a desire to get points on the board," said Hughes.
"We were excellent today. We got our noses in front but we made it nervous towards the end. The penalty miss put us on edge and we just needed to calm ourselves down after that."
Prior to Austin's penalty miss, James McArthur had gone close to equalising for the hosts - who were without the injured Wilfried Zaha - when his curling effort struck the crossbar.
At the other end, the brilliant Alex McCarthy - called up to the England squad this week - denied Palace striker Christian Benteke from close range after an earlier save from Luka Milivojevic's volley.
Saints' victory was Hughes' first at Selhurst Park in six attempts as a Premier League manager, and condemned the Eagles to a third consecutive league defeat.
Southampton arrived in south London having made a slow start to the season - a goalless draw with Burnley preceding consecutive defeats by Everton and Leicester.
And, though there is perhaps no immediate concern, a team that ended last season hovering precariously above the relegation zone need to start showing signs of progress.
Buoyed by their midweek win, Hughes' side took control of a first half that lacked any real quality, though Hennessey was alert on the occasions the energetic Ings and Shane Long did find a way through a well-drilled defence.
Saints returned from the interval with confidence, and Ings' well-executed goal looked to have set the tone for the visitors, who pressed in pursuit of a second.
But Austin's penalty miss gave Palace momentum and caused concern for Hughes, whose side have lost 24 points from winning positions since the start of the 2017-18 season.
As it was, his players held firm to keep the hosts out, before Hojbjerg sealed the win.
"In the first half we were in total control of the game and should have been a few goals to the good," said Hughes.
"We had to withstand a little bit of pressure but, if we keep playing at the level we're at, we'll get breaks and win games."
Zaha was a surprise omission from the Palace squad, with the club later revealing he had strained an abductor muscle in training on Friday.
That was five days after the 25-year-old became the Eagles' record Premier League goalscorer when he scored his 24th goal in the competition against Watford.
Without a player who had scored seven of their past nine league goals, Roy Hodgson's side failed to make a breakthrough against a resolute Saints defence.
Since the start of last season, Palace have lost all 10 Premier League games in which Zaha has not featured.
"He didn't play and again we didn't win. It's a pure fact that we have to learn to live with," said Hodgson.
Summer addition Jordan Ayew made his debut in place of Zaha, but it was Serbia international Milivojevic who went closest for the hosts in the first half with a lovely volleyed effort that McCarthy was equal to, before Benteke was denied a first goal from open play since January.
It is almost a year since Hodgson's appointment - the former England manager having replaced Dutchman Frank de Boer following a disastrous start to the season - and Palace have come a long way since.
But, having squandered numerous chances to level the match, they have now lost three league games in a row and will need to keep Zaha fit if they are to kick on this season.
"We shouldn't have got something out of the match," said Hodgson. "I was hoping after the penalty save we would show spirit and fight. They did show endeavour to get the equaliser but, over the 90 minutes, Southampton were the better team and deserved it."
The Premier League resumes in two weeks, following the first international break of the season.
Palace travel to Huddersfield on Saturday, 15 September (15:00 BST), while Southampton are at Brighton on Monday, 17 September (20:00).
Match ends, Crystal Palace 0, Southampton 2.
Second Half ends, Crystal Palace 0, Southampton 2.
Foul by Martin Kelly (Crystal Palace).
Charlie Austin (Southampton) wins a free kick on the left wing.
Goal! Crystal Palace 0, Southampton 2. Pierre-Emile Højbjerg (Southampton) left footed shot from the left side of the box to the centre of the goal. Assisted by Matt Targett following a fast break.
Attempt blocked. Patrick van Aanholt (Crystal Palace) left footed shot from the centre of the box is blocked. Assisted by Aaron Wan-Bissaka.
Attempt blocked. Max Meyer (Crystal Palace) right footed shot from the centre of the box is blocked. Assisted by Christian Benteke.
Corner, Crystal Palace. Conceded by Charlie Austin.
Attempt saved. Christian Benteke (Crystal Palace) header from very close range is saved in the centre of the goal. Assisted by Alexander Sørloth with a headed pass.
Corner, Crystal Palace. Conceded by Cédric Soares.
Attempt missed. Charlie Austin (Southampton) right footed shot from the left side of the box is high and wide to the right.
Ryan Bertrand (Southampton) wins a free kick on the left wing.
Foul by Martin Kelly (Crystal Palace).
Wesley Hoedt (Southampton) wins a free kick in the defensive half.
Foul by Christian Benteke (Crystal Palace).
Attempt missed. Christian Benteke (Crystal Palace) header from the centre of the box is too high. Assisted by Luka Milivojevic with a cross following a corner.
Corner, Crystal Palace. Conceded by Alex McCarthy.
Attempt saved. James McArthur (Crystal Palace) left footed shot from outside the box is saved in the top centre of the goal. Assisted by Cheikhou Kouyaté.
Attempt saved. Patrick van Aanholt (Crystal Palace) left footed shot from outside the box is saved in the top right corner. Assisted by Cheikhou Kouyaté.
Corner, Crystal Palace. Conceded by Ryan Bertrand.
Foul by Matt Targett (Southampton).
Aaron Wan-Bissaka (Crystal Palace) wins a free kick in the defensive half.
Foul by Pierre-Emile Højbjerg (Southampton).
James McArthur (Crystal Palace) wins a free kick in the defensive half.
Delay over. They are ready to continue.
Delay in match Ryan Bertrand (Southampton) because of an injury.
Ryan Bertrand (Southampton) wins a free kick in the defensive half.
Foul by Alexander Sørloth (Crystal Palace).
Foul by Matt Targett (Southampton).
James McArthur (Crystal Palace) wins a free kick in the defensive half.
Substitution, Southampton. Oriol Romeu replaces Danny Ings.
Attempt missed. Christian Benteke (Crystal Palace) header from the centre of the box misses to the left. Assisted by Max Meyer.
Jannik Vestergaard (Southampton) is shown the yellow card for a bad foul.
Foul by Jannik Vestergaard (Southampton).
Christian Benteke (Crystal Palace) wins a free kick in the attacking half.
Substitution, Crystal Palace. Alexander Sørloth replaces Jordan Ayew.
Substitution, Crystal Palace. Max Meyer replaces Jeffrey Schlupp.
Attempt blocked. James McArthur (Crystal Palace) right footed shot from outside the box is blocked. Assisted by Luka Milivojevic with a cross.
Corner, Crystal Palace. Conceded by Alex McCarthy.
Attempt saved. Cheikhou Kouyaté (Crystal Palace) right footed shot from outside the box is saved in the centre of the goal.