Match ends, Southampton 2, Manchester United 3.
Anthony Martial's dream Premier League start continued as the £36m striker scored twice to lift Manchester United to second with a win at Southampton.
United started poorly and went behind when Graziano Pelle converted a loose ball after David De Gea's fine save.
But Martial equalised with United's first shot on target and then took advantage of a terrible Maya Yoshida backpass to slot in a second.
Juan Mata added a third and while Pelle headed a late second, United held on.
Louis van Gaal's side were given a torrid time by the Saints in the opening half an hour but were once again clinical in front of goal.
United scored with all three of their shots on target against Liverpool last weekend and repeated the trick at St Mary's as Southampton - who have now won just two of their last 12 league games - slipped to defeat.
Lethal Martial gets Man Utd out of trouble
Wayne Rooney's poor start to the season as the leading man in United's attack led to a first league start for £36m signing Martial.
Rooney - with no goals or assists in the Premier League - started behind Martial and produced a laboured and largely anonymous display.
He - and Martial - had barely seen the ball in the final third as Southampton started superbly, before the Frenchman put United level.
Mata was offside in the build-up but Martial - who scored on his debut against Liverpool last week - again showed composure to turn Virgil van Dijk and fire home.
Martial became the third player to score on both of his first two Premier League appearances for United, after Louis Saha in 2004 and Federico Macheda in 2009. He finished coolly for his second when played through on goal by Yoshida's blind backpass.
In contrast to the incisive Martial, Rooney did not have a shot and has now not scored in the Premier League since 4 April, or scored an away goal in the league since last November.
Back in a deeper role he did play 56 passes, the fourth most of any player on the pitch.
How did United cope without Shaw?
Despite their win, Manchester United boss Van Gaal will be concerned by their slow start and in particular their defending.
United's reshaped back four looked a mess in the opening stages of their first game since left-back Luke Shaw suffered a broken leg in midweek.
Daley Blind had a torrid afternoon as he was bullied by Pelle, who was left unmarked to collect De Gea's fine save from Sadio Mane's volley to score the opener.
Minutes later Pelle again rolled Blind all too easily to thump a low shot against the post.
United regrouped but also missed Shaw going forwards, with stand-in left-back Marcos Rojo looking uncomfortable when attacking and crossing just twice.
The visitors ended up with only one member of their back four in their starting positions, as Antonio Valencia came on for Matteo Darmian at the break, and Patrick McNair replaced Rojo.
McNair and Smalling then both left Pelle totally unattended to head in his second of the game late on.
Retaining goalkeeper De Gea may yet prove to be United's key business this season, and he made brilliant saves from Jose Fonte and Victor Wanyama as Southampton mounted a late rally.
Man of the match - Anthony Martial (Manchester United)
Southampton manager Ronald Koeman: "The first 30 minutes we played perfectly, we had good organisation and they had difficulty breaking us.
"We lost it a bit 10 minutes before half-time. In the second half, if you make that kind of mistake it is impossible.
"We lost belief. The reaction after we made it 3-2 was good and we had enough chances but David De Gea made some good saves. We didn't lose because of Manchester United, we lost by ourselves."
Manchester United boss Louis van Gaal: "Anthony Martial is already special because we paid a lot of money for him. A lot of people are thinking he is a great star but he is a boy of 19. In three matches he has shown a lot.
"I am very happy with him but we and he have to keep our feet on the ground.
"That is why we were difficult in the transfer window. I have always said we wanted to keep David De Gea."
The stats you need to know
- United have scored from their last six shots on target in the Premier League
- All five league meetings between Ronald Koeman and Louis van Gaal have gone in favour of the away manager
- Juan Mata has been involved in four goals in his six league games this season
- 14 of Graziano Pelle's 16 league goals have come at home
- United have come from behind to beat Southampton on eight times in the Premier League - more than they have against any other opponent
What's next for both teams?
Southampton will look to get back to winning ways against Championship side MK Dons in the League Cup in midweek, before they host Swansea in the Premier League next Saturday.
Manchester United face Ipswich in a midweek cup match and could go top of the table next weekend. They play Sunderland at Old Trafford shortly after leaders Manchester City complete Saturday's early kick-off at Tottenham.
- 6José FonteBooked at 78mins
- 17van DijkBooked at 73mins
- 33TargettSubstituted forMartinaat 45'minutes
- 14RomeuSubstituted forDavisat 56'minutes
- 16Ward-ProwseSubstituted forLongat 76'minutes
- 2Cédric Soares
- 1de Gea
- 36DarmianSubstituted forA Valenciaat 45'minutes
- 5RojoSubstituted forMcNairat 69'minutes
- 16CarrickSubstituted forSchweinsteigerat 60'minutes
- 25A Valencia
- Mark Clattenburg
- Shots on Target
Second Half ends, Southampton 2, Manchester United 3.
Foul by Anthony Martial (Manchester United).
Victor Wanyama (Southampton) wins a free kick in the defensive half.
Attempt saved. Victor Wanyama (Southampton) header from the centre of the box is saved in the centre of the goal. Assisted by Virgil van Dijk with a headed pass.
Attempt saved. Jose Fonte (Southampton) header from the centre of the box is saved in the top centre of the goal. Assisted by Dusan Tadic with a cross.
Corner, Southampton. Conceded by David de Gea.
Attempt saved. Victor Wanyama (Southampton) left footed shot from outside the box is saved in the top left corner.
Attempt missed. Dusan Tadic (Southampton) with an attempt from the centre of the box is close, but misses to the left. Assisted by Sadio Mané with a cross.
Offside, Manchester United. Juan Mata tries a through ball, but Memphis Depay is caught offside.
Corner, Manchester United. Conceded by Maarten Stekelenburg.
Attempt missed. Graziano Pellè (Southampton) header from the centre of the box is high and wide to the right. Assisted by Shane Long with a cross following a set piece situation.
Foul by Antonio Valencia (Manchester United).
Victor Wanyama (Southampton) wins a free kick on the left wing.
Goal! Southampton 2, Manchester United 3. Graziano Pellè (Southampton) header from the centre of the box to the top right corner. Assisted by Sadio Mané with a cross.
Foul by Memphis Depay (Manchester United).
Sadio Mané (Southampton) wins a free kick on the right wing.
Delay over. They are ready to continue.
Delay in match Virgil van Dijk (Southampton) because of an injury.
Offside, Manchester United. Wayne Rooney tries a through ball, but Memphis Depay is caught offside.