Match ends, Liverpool 0, West Ham United 3.
West Ham won their first league match at Anfield since 1963 and inflicted a first loss of the season on Liverpool in a game featuring two red cards.
The Hammers produced a masterclass of counter-attacking football, with Manuel Lanzini impressing on his debut.
He scored the first and set up the second for Mark Noble, who became the second player sent off after Philippe Coutinho was red carded for Liverpool.
Diafra Sakho added a third for West Ham in injury time.
- Reaction to this match and the rest of Saturday's action
- Relive how West Ham won their first league game at Anfield in 52 years
They were the first goals of the season conceded by Liverpool, whose defence was a shadow of the one that had impressed against Stoke, Bournemouth and Arsenal.
From the sublime to the ridiculous
Liverpool have been rightly praised for the way their defence has performed to keep clean sheets in each of the first three Premier League games of the season.
However, the Reds' back four will deservedly be pilloried for their display against the Hammers.
Martin Skrtel's poor clearing header from a cross allowed Cresswell to pick the ball up and cross low for Lanzini to finish from close range to give the Hammers the lead.
Even worse was the dreadful mess made of a simple clearance by Dejan Lovren, who mis-controlled on his own byeline and allowed Lanzini to nip in and provide the half-cleared cross from which Noble followed up to slot in the second goal.
The moment made a mockery of the pre-match praise heaped on the £20m defender by Brendan Rodgers - who switched to a three-man defence in the second half to little effect, with Sakho punishing them a third time for hesitancy at the back.
Lanzini leads the charge
Liverpool's calamitous defending should not take away from West Ham's counter-attacking excellence, particularly in the first half.
In contrast to the diamond midfield utilised in the away win at Arsenal on opening day, the Hammers matched Liverpool's 4-3-3, but used the system to much better effect.
A committed and disciplined back four was protected superbly by the energetic trio of Pedro Obiang, Cheikhou Kouyate and Noble, allowing Dimitri Payet and Lanzini in particular the freedom to do damage in the Liverpool half, while Sakho led the line superbly.
Lanzini's debut showcased a willingness to pick up the ball deep and drive forward at pace and also an eagerness to work for the team by closing down opponents to force mistakes - something he did to optimum effect for the second goal.
In contrast, Liverpool's Roberto Firmino, brought in from Hoffenheim £29m in the summer, was a peripheral figure and was substituted after an hour.
The Brazilian was not the only Reds player to underperform, though, with Lovren's 55th-minute shot - easily saved by Darren Randolph - their only one on target.
Already trailing 2-0, Liverpool's challenge was effectively ended by the sending off of Coutinho - an outcome the Brazil midfielder could easily have avoided.
His first booking came from an indefensible lack of discipline as he failed to retreat from a free-kick, meaning any mis-timed tackle - like the one he produced on Payet in the 51st minute - left him vulnerable.
Not only did it cost Liverpool a realistic chance at getting something from this game but it means Rodgers will now have to cope without one of his best players, including in their next game against Manchester United.
There was a hint of controversy to Noble's straight red card, shown for violent conduct as a result of his lunging challenge on Danny Ings.
However, the whistle had already blown for a foul on Noble, which does not take away from his offence but does mean it came when play was not active.
Fortunately for him and his side, it came too late in the game to give Liverpool a chance to come back.
Man of the match - Manuel Lanzini
'We parked the bus but left the handbrake off'
West Ham boss Slaven Bilic: "We played really good and started well. We were well organised. We had a plan, but the boys perfectly did that plan. Their movement, concentration and aggression was 90% of the game.
"We parked the bus but we didn't put the handbrake on. There is nothing wrong with that. It means when the opponent has the ball you stop them. When needed we were there with nine men but when we had the chance we had players in their part of the pitch.
"With the greatest respect to the official, Mark Noble's sending off is not a red card."
Liverpool boss Brendan Rodgers: "We're disappointed with the result. We came into the game with a motivation to win but we give away a poor goal and you have to give credit to West Ham.
"We didn't defend moments well at all. We didn't have too many times to defend but when we did it wasn't how we've been. Offensively we weren't creative enough. We need to be much better than that.
"I didn't think Coutinho was a sending off and neither was the one for Noble."
Liverpool travel to Manchester United after the international break for a clash between two sides with top-four ambitions. United are at Swansea on Sunday and a win would leave them three points above Liverpool.
West Ham will hope to halt a run of two straight home defeats with a match against Newcastle at Upton Park.
The stats you need to know
- West Ham's win at Liverpool ends a run of 42 league Anfield visits without a victory.
- West Ham have been shown six red cards in 10 games this season in all competitions, compared to three in 43 last term.
- Manuel Lanzini's goal is the fastest scored in the Premier League so far in 2015-16, clocking in at two minutes and 28 seconds.
- West Ham had only 37% possession during the game and only 18% of it was spent in Liverpool's third.
- Liverpool mustered just one shot on target in this game; the third time that they have had just one shot on target at Anfield in a Premier League match since the start of last season.
- 2ClyneBooked at 90mins
- 12GomezSubstituted forIbeat 78'minutes
- 23CanSubstituted forMorenoat 45'minutes
- 21LeivaBooked at 70mins
- 11FirminoSubstituted forIngsat 61'minutesBooked at 86mins
- 10CoutinhoBooked at 52mins
- 16NobleBooked at 78mins
- 28LanziniBooked at 81minsSubstituted forOxfordat 82'minutes
- 15SakhoSubstituted forCullenat 90+6'minutes
- 27PayetSubstituted forJarvisat 88'minutes
- Kevin Friend
- Shots on Target
Second Half ends, Liverpool 0, West Ham United 3.
Substitution, West Ham United. Josh Cullen replaces Diafra Sakho.
Attempt blocked. Danny Ings (Liverpool) right footed shot from outside the box is blocked. Assisted by Lucas Leiva.
Attempt missed. Christian Benteke (Liverpool) header from the centre of the box misses to the right. Assisted by James Milner.
Goal! Liverpool 0, West Ham United 3. Diafra Sakho (West Ham United) left footed shot from the centre of the box to the bottom right corner.
Nathaniel Clyne (Liverpool) is shown the yellow card for a bad foul.
Foul by Nathaniel Clyne (Liverpool).
Aaron Cresswell (West Ham United) wins a free kick on the left wing.
Offside, West Ham United. Cheikhou Kouyaté tries a through ball, but Diafra Sakho is caught offside.
Substitution, West Ham United. Matthew Jarvis replaces Dimitri Payet because of an injury.
Delay over. They are ready to continue.
Delay in match Dimitri Payet (West Ham United) because of an injury.
Danny Ings (Liverpool) is shown the yellow card for a bad foul.
Foul by Danny Ings (Liverpool).
Dimitri Payet (West Ham United) wins a free kick in the attacking half.
Hand ball by James Milner (Liverpool).
Attempt missed. Dejan Lovren (Liverpool) right footed shot from the right side of the six yard box is high and wide to the right. Assisted by Christian Benteke with a headed pass following a corner.
Corner, Liverpool. Conceded by Pedro Obiang.
Corner, Liverpool. Conceded by Pedro Obiang.