Game overpublished at 17:00
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.
Liverpool XI: Mignolet, Clyne, Skrtel, Lovren, Gomez, Can, Lucas, Milner, Firmino, Benteke, Coutinho
West Ham XI: Randolph, Tomkins, Reid, Ogbonna, Cresswell, Kouyate, Obiang, Noble, Lanzini, Sakho, Payet
Phil Dawkes
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.
Liverpool 0-3 West Ham
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.
John Hartson
Former Wales striker on Final Score
"Slaven Bilic needed a result, and they've gone to Liverpool and thoroughly deserved that scoreline."
Diafra Sakho
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.
Matt Jarvis for Dimitri Payet
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.
Liverpool 0-2 West Ham
Dejan Lovren has a chance to make amends but pokes an effort wide at the far post following a head down from Christian Benteke.
Reece Oxford for Manuel Lanzini
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.
Liverpool 0-2 West Ham
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.
Jordan Ibe for Joe Gomez
Last change for Liverpool. Ibe has 12 minutes to make something happen.
Liverpool 0-2 West Ham
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 0-2 West Ham
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.
Liverpool 0-2 West Ham
Lucas lunges in on Mark Noble and picks up a card. That is born of frustration. No sign of a Liverpool comeback.
Liverpool 0-2 West Ham
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.
John Hartson
Former Wales striker on Final Score
"Coutinho is incredibly unfortunate. He's slipped, it's totally accidental - not a yellow card for me."
Liverpool 0-2 West Ham
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.
Danny Ings for Roberto Firmino
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.
Liverpool 0-2 West Ham
Darren Randolph finally has a save to make as Roberto Firmini drives from distance. He does it with minimal fuss.
Liverpool 0-2 West Ham
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.
Liverpool 0-2 West Ham
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.
Liverpool 0-2 West Ham
The game is back under way.