Jürgen Klopp found respite from a poisonous few days in the sanctuary of Anfield. Victory over Manchester City had offered a springboard for Liverpool’s Premier League campaign, something that was almost forgotten amid the fallout from Sunday, and they capitalised with a leap from Darwin Núñez and Alisson’s acrobatics. Liverpool’s £64m summer signing scored his first Anfield goal with a textbook header to deliver a second successive home league win. The goalkeeper, Alisson, secured it with a penalty save from West Ham’s Jarrod Bowen plus a crucial intervention when Tomas Soucek looked certain to equalise in the 87th minute. “Milly’s big toe”, as Klopp described James Milner’s tackle on the West Ham midfielder, also played its part in preserving both a clean sheet and the sense that Liverpool are gradually rediscovering their old momentum, spirit and resilience. But victory was far from straightforward. David Moyes’s visitors overcame a subdued start to take the game to Liverpool in the second half, when the introduction of Michail Antonio brought much-needed energy to the West Ham attack. For the second time in four days Liverpool held firm. “That we have space for improvement is clear,” said Klopp. “But we have three points more and it feels massive. We brought it over the line. We needed Ali and we needed Milly’s big toe. It was really important we brought it over the line in a tight game because that didn’t happen too often this season. It is not that we are used it – we either win really high or not – but it’s the second 1-0 in a row and that is absolutely fine.” Núñez was one of five changes from Sunday’s starting lineup and seized his opportunity. The Uruguay international had Anfield chanting his name long before opening the scoring with a fine centre-forward’s header beyond Lukasz Fabianski. He was replaced early in the second half as a precaution having felt a hamstring at half-time. The forward’s first chance came courtesy of an immaculate long ball over the top from Thiago Alcântara. Having let the ball bounce, the former Benfica player let fly and it needed a fingertip save from Fabianski to prevent a spectacular shot hitting the roof of the net. The West Ham goalkeeper had no chance of stopping Núñez’s next effort. Thiago was again involved, floating a ball into space on the left where Kostas Tsimikas collected, looked up and swept a superb cross into the heart of the visitors’ area. The delivery evaded Kurt Zouma but, before fellow central defender Thilo Kehrer could clear, Núñez ghosted in front and planted a downward header beyond Fabianski’s despairing dive. Núñez could have had a first half hat-trick. He shot straight at Fabianski after Fabio Carvalho had dispossessed Ben Johnson, then crashed a half-volley against a post having taken down Kehrer’s clearance expertly on his chest. West Ham arrived at Anfield on the back of a season-turning run of four wins and one draw in their last five games, yet struggled to retain possession or trouble Liverpool until the closing minutes of the first half. The visitors were handed a route back into the game when Joe Gomez leapt into the back of Bowen as they pursued a flick on into the Liverpool area from Flynn Downes. The referee, Stuart Attwell, initially ignored West Ham’s appeals for a penalty, to widespread astonishment, but was advised to check the pitch-side monitor by the VAR. All of Anfield knew what was coming, and perhaps not only when Attwell inevitably overturned his original decision and pointed to the spot. Bowen never looked confident as he shaped to take the spot-kick. Alisson, instrumental in Mohamed Salah’s winner against City, exuded the stuff and dived to his right to push away Bowen’s telegraphed penalty. West Ham showed far more adventure after the restart, albeit with Gianluca Scamacca toiling throughout, and could have levelled when an up-and-under from Declan Rice found substitute Saïd Benrahma unmarked behind Gomez at the back post. A tame volley, side-footed straight at Alisson, granted Liverpool a reprieve. The hosts’ rhythm was disrupted by five second half substitutions but Firmino, Jordan Henderson and Curtis Jones, on for his first appearance of the season, all went close to scoring a much-needed second. Henderson also had a low cross diverted on to his own crossbar by Zouma, who injured himself in the process. “That’s how your cat feels,” sang the Kop as the defender received lengthy treatment. With three minutes remaining Benrahma broke away from Trent Alexander-Arnold before crossing for Bowen, who controlled at the near post and dragged the ball back for Soucek. The goal was gaping, a point beckoned, but substitute Milner got a vital touch on the midfielder’s shot before Alisson deflected the ball wide with his thigh. Moyes slumped to the ground in disbelief. “I’m disappointed not to come away with anything when we had big opportunities to do so,” said the West Ham manager. “It’s the same story the last few times we’ve been here. I was hoping to change it tonight but we were not able to get it over the line.”