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It was not pretty, but West Ham will not care. Their five-game losing run is over.
For Swansea, they stay in the bottom three and they only have six matches left to save their Premier League status.
West Ham now have an eight-point cushion between themselves and 18th-placed Swansea.
Excellent defending from Sam Byram snuffs out a half-chance for Gylfi Sigurdsson. That could be it.
The West Ham fans are in good voice, and their side are three minutes away from a valuable three points.
Manuel Lanzini shows his silky skills to create some space for the cross. Jonathan Calleri slides in at the back post but can only hit the side netting. Still hope for Swansea. Five minutes injury time.
West Ham's Andre Ayew heads down into the ground from a good chance and that is his last action as Edimilson Fernandes comes on to replace him.
Now we're getting a better game. Andre Ayew forces a fine save from Lukasz Fabianski, who keeps the Swans in it.
A bright end to the game from the visitors. Where has this Swansea been? Substitute Jefferson Montero hares down the left wing and his cross takes a deflection off Mark Noble.
The ball loops over goalkeeper Darren Randolph but James Collins is well placed to acrobatically hack it clear.
They haven't deserved an equaliser, but they very nearly get one. Gylfi Sigurdsson's corner swings in from the left and goalkeeper Darren Randolph is nowhere near the ball. Leroy Fer is charging in at the back post but cannot get a touch that would have brought it level.
Moments later Luciano Narsingh unleashes an attempt from a tight angle. It looks like Randolph got his fingertips to it, to push it over, but the officials say it is a goal kick.
Corner to Swansea. Is this their moment?
Swansea are having to push men forward in the hope of an equaliser. They could be vulnerable on the counter atttack, and Federico Fernandez gets a yellow card for a cynical foul on Andre Ayew.
Manuel Lanzini takes the free-kick but it is just over the top.
It's fair to say this has not been a classic. Can Swansea get back into this one?
West Ham have a free-kick in a dangerous position. Manuel Lanzini takes it but Fernando Llorente is there at the near post to head it clear.
Feghouli nearly makes an instant impact as his low cross finds Jonathan Calleri, but, under pressure, his dinked effort is deflected over the bar.
We have not had many chances in what has been a low-key second half. Mark Noble goes for an optimistic one, 30 yards out, but it is straight at Lukasz Fabianski.
The Hammers then make a change with Sofiane Feghouli coming on. A very annoyed Robert Snodgrass is the man to come off.
Jordan Ayew has been one of a few plus points for Swansea today. He is certainly putting in the effort, but runs into a dead end as he aims to get into a position to cross. Swansea need to do more.
Swansea have now used up all three substitutes with more than 25 minutes of the game remaining.
Jack Cork cannot carry on and is helped off the pitch by two of Swansea's medical team after an ankle injury. Jefferson Montero is the man who replaces Cork.
Swansea have not had the best of days and now Jack Cork needs some medical attention after landing badly on his ankle when jumping for a challenge
Embarrassing from West Ham's Manuel Lanzini who throws himself to the ground in the penalty area, under no contact from Federico Fernandez - the defender closest to him.
Lanzini is rightly cautioned for a shameful piece of play-acting.
It has been better from Swansea since the restart and the introduction of Llorente. Swans fans will also hope it leads to an improved performance from Gylfi Sigurdssson who had a surprisingly quiet first half.
Some brave defending from James Collins keeps the hosts ahead. A cross is played into the area, Leroy Fer lays it off and substitute Luciano Narsingh nearly makes an immediate impact.
Unluckily for him, Collins throws himself in front of the shot for a vital block.
An early chance at the start of the second half. West Ham's Andre Ayew produces some good work and the ball falls to Sam Byram, but from a tight angle, he can only shoot into the side netting.
Yullaw: I would rather watch West Ham vs Swansea than Real Madrid vs Athletico Madrid! Premier League football is much more intense.
Paul Clement needed to do something, and he has taken action. Fernando Llorente, who missed two games with an ankle injury, is on, as is Luciano Narsingh. Wayne Routledge and Tom Carroll are off.
It means Llorente goes up front, with Sigurdsson moving to the 'number 10' role.
The Swansea Twitter account sums up a poor first first half from their team.
Match of the Day commentator
What a very good goal from Kouyate to separate the sides. It has lifted the place and gives Slaven Bilic a more comforting half-time team talk.
A lovely goal for the hosts. Mark Noble, 40 yards out, plays a pass into Robert Snodgrass, who produces a neat touch to give it to Cheikhou Kouyate.
The powerful midfielder is able to run at the Swansea defence and unleash a great low strike from 25 yards out which finds the bottom corner. A deserved lead for the Hammers.
A great strike.
Gylfi Sigurdsson's floated free-kick clears the wall but it does not have enough pace to cause West Ham's Darren Randolph any problems, and it is easily dealt with by the home goalkeeper.
Mark Noble is booked for conceding a foul on the edge of his own penalty area for a lunge on Leroy Fer.
Noble is unhappy that the game was not stopped after Michail Antonio sharply pulled up with what looks a hamstring injury.
Antonio's game is done, which is a big loss for the Hammers. Jonathan Calleri will come on to defend the free-kick.
Swansea have had more of the possession recently, but they have still not tested Darren Randolph.
They nearly have a chance when Jordan Ayew swings in a low cross from the right flank, but the ball is just ahead of Gylfi Sigurdsson.
Yet again West Ham are denied by Lukasz Fabianski. The ball is given away by Swansea defender Alfie Mawson and Mark Noble releases Andre Ayew.
He curls an effort at goal and it is going inside the post, before Fabianski, at full stretch, gets a hand to it to keep it out. Excellent stop.
The best moment of the game from Swansea. Jordan Ayew gets to the byeline and pulls a cross back into the area but James Collins is there at the front post to stab the ball clear.
Swansea fans need to see more from their side as an attacking force. Darren Randolph in the West Ham goal has hardly had a touch, with Swansea's Jordan Ayew and Gylfi Sigurdsson anonymous so far.
Another effort for West Ham. This time Manuel Lanzini wriggles free to shoot at goal from 25 yards, but the radar is a bit off and it goes over the bar.
So nearly the first goal of the game. Sam Byram gets down the right wing and crosses for Michail Antonio. He is able to dink the ball back into the middle and the delivery is met by a Robert Snodgrass header.
Luckily for Swansea, Lukasz Fabianski does well to get down quickly to save the close-range header on the goalline.
That would have been a first goal for West Ham for Snodgrass following his move from Hull during the January transfer window.
Not much from the visitors so far today. No shots, no corners, not much of the ball, but we're still goalless.
Another promising position for West Ham as Andre Ayew leads the charge on the right wing, but the final ball, chipped into the box, is wasted and easily gathered by Lukasz Fabianski.