Head on over to our main live page to follow the reaction to this game and all the rest of today's Premier League matches.
It has been a long time coming for West Ham but they have their first victory at Anfield since 1963. It was fully deserved as well.
Liverpool had been so solid until today, but their own defensive mistakes, coupled with some incisive Hammers attacking led to their undoing.
The red cards will occupy some column inches but today should be all about a superb away display from West Ham.
Former Wales striker on Final Score
"Slaven Bilic needed a result, and they've gone to Liverpool and thoroughly deserved that scoreline."
If there was any doubt the points weren't heading to West Ham, it has been wiped out now. Diafra Sakho, who was a doubt to even play here after his arrest two months ago, fends off the attention of a number of Liverpool defenders and then slots a low shot into the corner. Anfield is emptying fast.
Another West Ham change sees Matt Jarvis come on for Dimitri Payet. Surely West Ham have this game in the bag now. The Liverpool players look flat.
Dejan Lovren has a chance to make amends but pokes an effort wide at the far post following a head down from Christian Benteke.
The 16-year-old comes on to give West ham greater numbers in the defensive part of their midfield and Manuel Lanzini, who has just been shown a yellow card, departs.
The teams have been evened up. It is a controversial moment as well as Mark Noble slides in on Danny Ings with his studs up and gets a straight red. Noble complains, mainly because the whistle had already gone for a foul on him.
This gives Liverpool a sniff.Copyright: Getty Images
Last change for Liverpool. Ibe has 12 minutes to make something happen.
Oh, it's nearly 3-0. Aaron Cresswell turns Joe Gomez inside out and then fires a shot from an angle in the box but Simon Mignolet saves at his near post. Three West Ham corners follow, with the last headed wide of goal by Winston Reid. That would have killed the game stone dead.
Liverpool have a free-kick wide right. Milner can deliver into the box. He does so and Christian Benteke rises to meet it but the whistle has gone for a foul on a Hammers defender. The groans of the home crowd have gone from outraged to resigned acceptance.
Lucas lunges in on Mark Noble and picks up a card. That is born of frustration. No sign of a Liverpool comeback.
Danny Ings looks bright. He charges into the box to try and reach a one-two pass with Christian Benteke but Darren Randolph slides out to claim just ahead of the former Burnley man. The two-man attack is giving Liverpool more options up front, but the Reds need to score soon if they are going to make West Ham wobble.
Former Wales striker on Final Score
"Coutinho is incredibly unfortunate. He's slipped, it's totally accidental - not a yellow card for me."
James Milner with a chance for Liverpool! The ball drops to him on the edge of the box off the boot of Danny Ings but the England man pulls his shot wide. Huge chance. Gone.
West Ham looking to strangle the life out of this game now. Cheikhou Kouyate challenges Simon Mignolet and takes a knock, dropping to the floor and ensuring play is broken up. In the meantime, on comes Danny Ings for his Liverpool debut in place of the ineffective Roberto Firmino.
Darren Randolph finally has a save to make as Roberto Firmini drives from distance. He does it with minimal fuss.
Now Liverpool are in big, big trouble. Philippe Coutinho, who was booked for dissent in the first half is shown a second yellow and then red card for sliding in on Dimitri Payet. It was a stupid challenge following an even more stupid failure to retreat from that free-kick before the break. Liverpool had a mountain to climb before, but now they'll have to do it without their strongest climber.Copyright: Getty Images
Take a bow Alberto Moreno. In his first meaningful action, the substitute dives in to prevent Cheikhou Kouyate getting in on goal during a West Ham break.
You suspect that will be the theme of this half as Liverpool press forward and the Hammers look to hit on the counter.
The game is back under way.
Change for Liverpool as Can departs, surely through injury, and Moreno comes on. It will mean a change of system as well. Three at the back now for the home side.
BBC Radio 5 live senior football reporter at Anfield
"The scoreline at Anfield is no fluke. Liverpool's defence has been talked up but they've been breached twice and a mistake from Dejan Lovren for one of them will get plenty of attention."
What a superb half from West Ham. They have harried, hassled and taken their chances when they came. In contrast, Liverpool have looked shambolic at one end and short of ideas at the other. They need to change something, and fast.
Liverpool have a corner to finish the half. James Milner takes it short and Philippe Coutinho loses the ball. That sums it up for the home side, who get a barrage of stick from their own fans.
To rub salt in Coutinho's wounds, he gets yellow carded soon after for not retreating from a free-kick.
Injury time. West Ham sitting pretty.
As you can see, Roberto Firmino has not had much involvement in the game so far...Copyright: Opta
Roberto Firmino's afternoon so far is summed up by him over-hitting a simple pass from the edge of the box to try and set up a cross for Nathaniel Clyne straight out of play. Big groans now from the frustrated home fans.
This game is going completely to plan for one of these sides. And it is not Liverpool.
Superb defending from West Ham as Philippe Coutinho looks to buy space for a shot but finds the door close as quickly as it was briefly edged open. Winston Reid and Angelo Ogbonna are rock solid at the moment.
Daniel Sturridge is suited and booted and in the stands at Anfield. He is reportedly close to returning to action. How Liverpool could do with him now. They've not had any punch in the West Ham box so far.
Mark Noble slides in on Emre Can. The West Ham midfielder limps away with a yellow card to his name.
Mark Noble is understandably full of confidence at the moment. He attempts a long-range volley but misses the target by plenty. Still, worth a gamble when your side are two goals up.
Former Wales striker on Football Focus
"Take nothing away from Mark noble's finish - he opens up his body and sidefoots it past Mignolet. It's a brilliant finish."
Dejan Lovren what were you doing? You can see on the goal graphic below how he loses the ball on the bye-line, allowing Manuel Lanzini to find goalscorer Mark Noble.Copyright: Opta
James Milner is lucky to avoid a yellow card as he lunges in to fell Cheikhou Kouyate on the edge of the West Ham box. The Hammers player needs some treatment but he will be OK. It would take an almighty crowbar to remove one of the West Ham players from this match now.
Dejan Lovren, what have you done?! He gets in an almighty mess trying to control the ball on his own bye-line and allows Manuel Lanzini to nick the ball. The resulting low cross is cleared before Diafra Sakho can finish but Mark Noble makes no mistake with a follow-up finish, which he steers into the bottom corner of the net.
Liverpool's defending has gone from the sublime to the utterly ridiculous. West Ham boss Slaven Bilic affords a tiny smile. Inside he must be doing somersaults!Copyright: Getty Images
West Ham on the break and Aaron Cresswell finds himself with space to shoot from the edge of the box but gets the ball under his feet and can only poke an effort over.
Liverpool may be having most of the play, but West Ham look dangerous on the break.
Another corner for Liverpool, who continue to push forward. Christian Benteke feels he was being held as James Milner delivers but the referee ignores his protests as West Ham clear.
Liverpool corner. Their first. James Milner takes it but Dejan Lovren is penalised for a foul. He practically tore the shirt off his marker's back.
Emre Can with a dream of a first touch to bring down a long pass on the right sets up Lucas for a low cross that is aimed for Christian Benteke but cleared by West Ham. The home side are blowing hard but that Hammers house is still standing.
The classic away-day display early on from West Ham? The average positions graphic below (West Ham on the right) shows the Hammers have been mostly defending. They still lead though...Copyright: Opta
End to end. Emre Can finds Nathaniel Clyne on the right but a combination of two West Ham defenders, setting Manuel Lanzini on a charge which ends with a shot just past the post from the edge of the box. He looks a useful player, this kid. Very positive.
More jangling nerves for the home side at Anfield. West Ham are really testing this new-found defensive solidity. Martin Skrtel gets underneath an Aaron Cresswell cross to concede a corner and then Christian Benteke rises highest to head clear from the resulting delivery. He was fouled in the process.
Jason Roberts on Final Score: "Joe Gomez has got to do better. That's the difference between a goal and keeping a clean sheet - making sure Lanzini doesn't get across him there."
Oh, so close for Roberto Firmino! He turns one way, then the next before unleashing a shot from 25 yards that Darren Randolph is nowhere near but is very relieved see hit the post and go wide. So near to a home debut goal for the Brazilian.
Soon after, Christian Benteke goes down in the box under a challenge from Winston Reid but the referee just carries on running. No penalty.Copyright: Reuters
Anfield is shell-shocked. This wasn't in the script. The home side try to get their way back into the game but Philippe Coutinho's shot is sliced high and wide, followed soon after by mocking cheers from the away end.
Liverpool boss Brendan Rodgers is already scribbling furiously in his notebook.
What a start for West Ham as Manuel Lanzini opens the scoring at Anfield - as shown below.Copyright: Opta
How do you make an impression with a new club? Just like this! The Hammers lead through Manuel Lanzini's close-range finish, on his first start. It is a poor Martin Skrtel header that allows Aaron Cresswell to cross low into the box and Lanzini to finish.
This is the first goal a West Ham player has scored at Anfield in over nine years. And the first Liverpool have conceded in the league this season. What a start!Copyright: Getty Images
Emre Can has space to cross from the right but James Tomkins does well to chest back to Darren Randolph, in for the suspended Adrian in the Hammers' goal.
And we are under way.
That West Ham bench really is young. The front row looks like it's populated by a boy band.
The teams are out. Kick-off in a tick...
Match of the Day commentator
"Just three games in to the new season and already there's a cautious optimism sweeping around Anfield and an anxious pessimism enveloping the east-end.
"Yet to concede, Liverpool look hard to beat with a solid defence providing the platform for their flair players to prosper. Significantly, all the new signings have settled in quickly this time.
"West Ham's opening weekend win at Arsenal already resembles a false dawn. Home defeats by Leicester and Bournemouth have brought them crashing back to earth.
"There's not much depth to the squad and already there are signs of unrest. It could be a long season."
- Copyright: AFP
So what about West Ham then? Well, it is clear that they have some work to do before the window closes. The release of Kevin Nolan and the presence of four inexperienced teenagers on their bench today is a testimony to that.
They were very well organised at Arsenal on the opening day but were often shambolic against Bournemouth last week, conceding four to the newly-promoted Cherries.
Which version of the Hammers will we see today? A lot will depend on how Noble, Obiang and Kouyate cope with the midfield three of the home side and whether they can keep Philippe Coutinho quiet.
Some players get plenty of plaudits, but some sit under the radar, mainly impressing the people who matter. Emre Can is somewhat in the latter camp. He goes about his business with minimum fuss and this has been recognised this week through a call-up for Germany - his first.
“Emre had a good development at Liverpool and is a versatile player. We like his presence on the pitch and his dynamism,” said Germany coach Joachim Low said. “Now we want to get to know him a bit better.”
Brendan Rodgers has been full of praise for one of those Liverpool defenders who has helped them keep three clean sheets this season; Dejan Lovren.
The Croatia centre-back was hammered last season for a string of poor displays following his arrival from Southampton. But he is now starting to look something like a £20m player.
"He’s much more patient in his game now, he’s got the stability of playing," said Rodgers. "He’s in the team and he’s in because he had a good pre-season so he’s in good condition. He’s focused but he’s also a bit more relaxed in his position.”
- Copyright: BBC
Key to Liverpool's positive start to the season has been their solid defence. Both of their victories have come by a single goal, while the Reds back four had to be on the ball to keep Arsenal at bay at the Emirates (although they also needed a bit of held from the officials!).
A fourth consecutive clean sheet today will equal the club’s record from the start of a league campaign, achieved a decade ago.
Think you can guess the outcome of this match? Have a go at our predictor game and you'll get a video message from one of the Match of the Day pundits at the end of the weekend rating your performance.Copyright: .
- Copyright: .
Liverpool manager Brendan Rodgers names an unchanged starting line-up from the side that drew 0-0 with Arsenal on Monday.
Liverpool XI: Mignolet, Clyne, Skrtel, Lovren, Gomez, Lucas, Can, Milner, Firmino, Coutinho, Benteke
West Ham boss Slaven Bilic makes two changes to the side that lost 4-3 at home to Bournemouth last Saturday. James Tomkins replaces the suspended Carl Jenkinson at right-back, and midfielder Miguel Lanzini comes in for Kevin Nolan, who has left the club by mutual consent.
West Ham XI: Randolph, Tomkins, Reid, Ogbonna, Cresswell, Obiang, Kouyate, Lanzini, Noble, Payet, SakhoCopyright: .Copyright: .
- Copyright: Getty Images
Three games, seven points, no goals conceded; it would be fair to say Liverpool have started this season in more pleasing fashion than they ended the last.
Wins over Stoke and Bournemouth and a goalless draw at Arsenal have given Reds fans reason to hope the 2014-15 season was the abnormality, as opposed to the previous campaign's title challenge.
In contrast, West Ham fans have gone from cock-a-hoop to concerned in the space of three weeks. Following up an opening win at Arsenal with home defeats by Leicester and Bournemouth means they may well be happy to be on the road again.