Match ends, Southampton 0, West Ham United 1.
West Ham boss Manuel Pellegrini says he "never lost trust in what we do" after a deserved win at relegation rivals Southampton which could ease some pressure on him.
The Chilean could reportedly have lost his job had they lost, following a run of only one win in 11 games.
"I don't read the media but I am not stupid," he told BBC Sport. "If you don't get results, if you have five points from 30, you're in a difficult moment."
Sebastien Haller scored the only goal from Pablo Fornals' knock-down in the first half.
The Hammers - who had a strong penalty appeal turned down by the video assistant referee - thought they had doubled their lead through Michail Antonio but his goal was ruled out by the VAR for handball.
Saints improved after the break and Danny Ings hit the woodwork twice - although the offside flag had gone up for one of them - and he then had a goal ruled out for a Moussa Djenepo foul.
"I can't divide myself from the team," said Pellegrini. "For West Ham it was an important three points.
"I said before the game that I felt every day the commitment of the players in the work that they do. I am happy for the players. We started the season very well and I hope now we have recovered our best performance for the next games."
Southampton - whose manager Ralph Hasenhuttl is also under pressure - remain in the relegation zone, with the Hammers now four points clear in 15th place.
"To stay in the league we need to win these home games against these type of opponents," said the Saints manager.
West Ham boost morale despite VAR controversies
West Ham's struggles are perhaps best illustrated by the fact Haller is their top scorer despite this goal - only his second since August - ending an eight-game drought.
The Hammers had only won once in their past 11 games in all competitions but Pellegrini's side put in one of their best performances of the past couple of months, with Antonio and Haller lively up front.
The London side started on the front foot, with Declan Rice having a header from Robert Snodgrass' free-kick rightly disallowed for offside in the opening two minutes.
West Ham then had a penalty appeal - in fact two penalty appeals in one - turned down. Ryan Bertrand appeared to push Haller as Jan Bednarek was grappling with Antonio at the same time - but the VAR did not give a penalty for either.
"I was in a headlock and he got pushed," said Antonio afterwards.
West Ham fully deserved the breakthrough when Antonio kept the ball in play and pulled it back for Snodgrass, whose cross was headed back by Fornals to Haller to smash home a shot on the bounce.
It looked as if it was 2-0 when Antonio controlled the ball, blocked Bednarek's clearance and blasted in. But VAR discovered that Antonio had used his hand in the initial bit of control. West Ham players and fans were furious but this season's handball laws mean that you cannot use your hand and then score even if it was accidental.
"I think I'm going to cut my hands off," Antonio said. "It happened to me at Chelsea and it happened to me today. It is like they are magnets or something."
The Hammers did not look quite so comfortable after the hour mark, although Haller almost doubled their lead with a fine header wonderfully saved by Alex McCarthy.
But West Ham saw the game out for only a second win since beating Manchester United on 22 September.
There was a worry at the end as David Martin hurt himself while taking a goal-kick in injury time but he played the final seconds because the visitors had already made three substitutions.
Saints struggle despite Ings' best efforts
Southampton looked as if they might have turned the corner with 2-1 wins against relegation rivals Watford and Norwich in their past two home games.
But they are back to square one, having also lost at Newcastle last time out.
They only managed two shots on target against West Ham, with neither Shane Long's header nor James Ward-Prowse's 20-yard shot really threatening Martin.
Hasenhuttl - who had gone to a 4-4-2 formation in recent weeks - made a system change at half-time, bringing on midfielder Oriel Romeu for winger Nathan Redmond - and they were better afterwards, but still not good enough.
"We took more risks in the second half - we had to," Hasenhuttl told BBC Sport.
It would have been a smash and grab had Ings scored when he controlled Djenepo's cross before rifling a shot off the crossbar. Long turned the rebound wide.
The former Liverpool striker, who had scored in his previous five games, then hit the post after latching onto a long ball. The offside flag had gone up - although he appeared to be onside so it is likely a goal would have been given by VAR had he hit the back of the net.
He did finally beat Martin with a fine 20-yard curling effort but the whistle had already gone for a foul by Djenepo - again a debatable decision.
But Southampton, who have only scored 18 goals and conceded 36 this season, will need to play better than this if an eight-season stay in the Premier League is going to be extended.
"We know we have a difficult situation but we have seen a team fighting for three points but today we were not good enough," said Hasenhuttl.
"We knew it would be a very tough game for us. In the first half we had big problems with the long balls. We changed it at half-time and in the second half I thought we had the better chances.
"I saw a team fighting until the end and fighting to turn the tables but it was not possible for us. We need to fight more and try to win more."
Match stats - Pellegrini second to Curbishley
- West Ham have won more Premier League games against Southampton than they have against any other side (17).
- Southampton have conceded at least once in their past 14 Premier League home games, the longest run without a home clean sheet in the competition since Crystal Palace's 15 in May 2015.
- West Ham have won a league-high 63% of their Premier League points this season in away games (12/19).
- Sebastien Haller scored his first goal in the Premier League since netting against Crystal Palace in October, ending a run of 636 minutes without scoring in the top flight.
- Pablo Fornals has provided three assists in his past four Premier League games - as many as he had in his previous 48 appearances in the top five European leagues.
- West Ham have kept six clean sheets in 28 games away from home in the Premier League since the start of last season. Despite starting just three of those games, goalkeeper David Martin has kept two of them.
- Of all permanent West Ham managers in the Premier League, only Alan Curbishley (37.1%) has a higher win ratio than Manuel Pellegrini (36.4%).
Man of the match - Michail Antonio
West Ham are not in action again until 26 December - a trip across London to Crystal Palace (15:00 GMT) - because their game against Liverpool was postponed with the Premier League leaders in the Club World Cup.
Southampton visit relegation rivals Aston Villa next Saturday and host Chelsea on Boxing Day (both 15:00 GMT).
- 2Cédric SoaresSubstituted forAdamsat 87'minutes
- 23HøjbjergBooked at 37mins
- 22RedmondSubstituted forRomeuat 45'minutes
- 7LongSubstituted forArmstrongat 84'minutes
- 25MartinBooked at 90mins
- 24FredericksBooked at 56mins
- 11SnodgrassBooked at 45minsSubstituted forYarmolenkoat 73'minutes
- 16NobleSubstituted forDiopat 88'minutes
- 22HallerSubstituted forC Sánchezat 79'minutes
- 15C Sánchez
- Martin Atkinson
- Shots on Target
Second Half ends, Southampton 0, West Ham United 1.
David Martin (West Ham United) is shown the yellow card.
Corner, Southampton. Conceded by Ryan Fredericks.
Jan Bednarek (Southampton) wins a free kick in the defensive half.
Foul by Andriy Yarmolenko (West Ham United).
Attempt saved. James Ward-Prowse (Southampton) right footed shot from outside the box is saved in the centre of the goal.
Moussa Djenepo (Southampton) wins a free kick in the attacking half.
Foul by Fabián Balbuena (West Ham United).
Substitution, West Ham United. Issa Diop replaces Mark Noble.
Oriol Romeu (Southampton) wins a free kick in the attacking half.
Foul by Michail Antonio (West Ham United).
Substitution, Southampton. Che Adams replaces Cédric Soares.
Attempt missed. Pierre-Emile Højbjerg (Southampton) right footed shot from the centre of the box is close, but misses to the left. Assisted by Moussa Djenepo.
Substitution, Southampton. Stuart Armstrong replaces Shane Long.
Moussa Djenepo (Southampton) wins a free kick on the left wing.
Foul by Pablo Fornals (West Ham United).
Corner, West Ham United. Conceded by Moussa Djenepo.
Attempt missed. Jack Stephens (Southampton) right footed shot from the centre of the box misses to the right. Assisted by Pierre-Emile Højbjerg.
Substitution, West Ham United. Carlos Sánchez replaces Sébastien Haller.