Liverpool secured back-to-back Premier League wins thanks to Darwin Nunez and Alisson Becker.
Uruguay forward Darwin planted home a fine header from a Kostas Tsimikas cross midway through the first half for his first Anfield goal, settling nerves after an even start.
The former Benfica man smashed an effort off the post as Liverpool searched for a second, and the Reds then had Alisson to thank for a penalty save from Jarrod Bowen just before half-time.
Jordan Henderson and Roberto Firmino came close to doubling Liverpool's lead in the second half, before Alisson - who assisted Mo Salah in the win over Man City at the weekend - brilliantly saved from Tomas Soucek to maintain Liverpool's lead.
Here are the Reds' winners and losers from a tense night.
Winners
Darwin Nunez
There was a tweet that went semi-viral after the Manchester City game on Sunday which declared that *this* is what it's like watching Liverpool's major summer signing play football, and it was accompanied with all of the comedy cartoon sound effects you can imagine, the type of thing you'd see when Wile E. Coyote crashed into a wall as he was chasing Road Runner.
And while the Uruguayan has certainly attracted more than his fair share of criticism from fans of Liverpool's rivals - which online seems to be basically everyone these days - these tweets were being shared by Reds fans, and many with a funny or motivational message attached.
You can debate the merits of a side who were a few kicks away from football perfection last season choosing to take on a project like this - and Darwin is certainly that - at a time when they are, or were, so on the coattails of City, but boy is it a compelling project, and inside Anfield at least the fans are on board.
Right from the start the forward was smashing into West Ham's defenders, bringing others into play and generally being an absolute nuisance, and it was effective.
His fine header from Tsimikas' cross opened the scoring at a time when Liverpool needed to do just that, and he could have had a second in the second half when he crashed his effort off a post.
He may look like a footballer who needs sound effects, but he's one you can't stop watching.
Alisson
Get yourself a man who can do both.
The focus in the past few days might have been on Alisson's assist for Mo Salah which won the game against City, but here was the Brazilian showing that he can do the conventional goalkeeper things as well.
Sure the penalty from Bowen - who had had to wait a long time in front a vociferous Kop following a marginal VAR call - was at a good height for the stopper, but coming when it did just before half-time proved crucial for Liverpool's confidence, as a setback then, just as West Ham improved, could have been key.
Alisson has probably been Liverpool's most consistent player during the frequent mess of the season, with Andy Robertson even admitting recently that the squad feel as though they've been letting their No. down.
He stood up for them here, again making a vital save late on, and this three points was largely down to him.
Losers
Joe Gomez
When teams play against Liverpool they have to choose which side of the Reds' defence they are going to attack, and one of those sides has Virgil van Dijk on.
That is one of the reasons why the often revolving door to the right of the Dutchman can be so susceptible to form and fitness issues, with the strain placed on that player often greater than the burden that is placed on his illustrious teammate.
Gomez's injury issues have usually been more down to bad luck than any repetitive strain, but after playing so well against City he'll be desperate for a run in the side now.
However he looked slightly nervous here as he sought to deal with the giant Italian Gianluca Scamacca, and it was Gomez who clumsily tripped Bowen for the Hammers penalty.
He can be excellent as he showed against City, but this wasn't one of his better nights.
Fabinho
It is partly to do with the change in formation, but the Brazilian no longer has the authority of a player who is one of the first names on Liverpool's teamsheet.
He had one of his better games of the season in the win over City, but instead of backing that up with another start Klopp put him on the bench here.
He did enter the game before the hour mark, but he seems some way off his best at the moment and is repeatedly scratching for form.
Contrast that to another silky display from Thiago Alcantara and a fine one from Jordan Henderson and you can see a hierarchy forming.
