Liverpool’s £64m summer signing scored his first goal at Anfield with a header in the book to seal a second straight home league win. Goalkeeper Alisson made sure of it with a penalty from West Ham’s Jarrod Bowen plus a crucial save when Tomas Sucek looked certain to equalize in the 87th minute. “Millie’s big toe”, as Klopp described James Milner’s tackle on the West Ham midfielder, also played his part in keeping the clean sheet and the sense that Liverpool are gradually rediscovering their old momentum, her spirit and resilience. But the victory was far from simple. David Moyes’s visitors overcame a sluggish start to take the game to Liverpool in the second half when the introduction of Michail Antonio brought much-needed energy to West Ham’s attack. For the second time in four days, Liverpool held firm. “That we have room for improvement is clear,” Klopp said. “But we have three points more and it’s huge. We brought it over the line. We needed Ali and we needed Millie’s big toe. It was really important that we got it over the line in a tight game because that hasn’t happened very often this season. It’s not that we’re used to it – whether we win very high or not – but it’s the second 1-0 in a row and that’s absolutely fine.” Núñez was one of five changes from Sunday’s starting line-up and took his chance. The Uruguay international had Anfield chanting his name long before he opened the scoring with a fine cross-forward header past Lukasz Fabianski. He was substituted early in the second half as a precaution having felt a hamstring at half-time. The striker’s first chance came courtesy of a superb long ball over the top from Thiago Alcantara. After letting the ball bounce, the former Benfica man let fly and it took a fingertip save from Fabianski to prevent a spectacular shot hitting the roof of the net. Jarrod Bowen’s penalty in the first half was saved by Liverpool’s Alisson. Photo: Jon Super/AP The West Ham keeper had no chance of stopping Nunez’s next effort. Thiago was involved again, flicking a ball into space on the left where Kostas Tsimikas gathered, looked up and swept a superb cross into the heart of the visitors’ box. The delivery eluded Kurt Zouma but, before fellow centre-back Thilo Kehrer could clear, Núñez flashed forward and headed low beyond Fabianski’s desperate dive. Núñez could have had a hat-trick in the first half. He shot straight at Fabianski after Fabio Carvalho had dispossessed Ben Johnson, then crashed a half-volley onto the post having deftly knocked down Kerrer’s gap on his chest. West Ham arrived at Anfield on the back of a run of four wins and a draw in their last five games but struggled to keep possession or trouble Liverpool until the final minutes of the first half. The visitors were given a route back into the game when Joe Gomez pounced on the back of Bowen as they pursued a move into the Liverpool area from Flynn Downes. Start your evenings with the Guardian’s view of the world of football Privacy Notice: Newsletters may contain information about charities, online advertising and content sponsored by external parties. For more information, see our Privacy Policy. We use Google reCaptcha to protect our website and Google’s Privacy Policy and Terms of Service apply. The referee, Stuart Atwell, initially ignored West Ham’s appeals for a penalty, much to their surprise, but was advised to check the pitch-side monitor by VAR. All of Anfield knew what was coming, and perhaps not least when Atwell inevitably overturned his original decision and pointed. Bowen never looked confident as he planned to take the spot-kick. Alisson, who played a key role in Mohamed Salah’s winner against City, breathed things out and dived to his right to put away Bowen’s telegraphed penalty. West Ham showed much more adventure after the restart, albeit with Gianluca Scamaka toiling throughout, and could have leveled when a Declan Rice lofted ball found substitute Saïd Benrahma unmarked behind Gomez at the back beam. A tame volley, side-footed straight at Alisson, gave Liverpool a reprieve. The hosts’ rhythm was disrupted by five second-half changes but Firmino, Jordan Henderson and Curtis Jones, on his first appearance of the season, came close to scoring a much-needed second. Henderson also had a low cross deflected onto his own post by Zouma, who was injured in the process. “That’s how your cat feels,” sang the Kop as the defender received lengthy treatment. With three minutes remaining Benrahma was cut out by Trent Alexander-Arnold before passing to Bowen, who controlled at the near post and slid the ball back for Sucek. The goal was wide open, a point beckoning, but substitute Milner got a vital touch on the midfielder’s shot before Alisson deflected the ball wide with his thigh. Moyes crumpled to the ground in disbelief. “I’m disappointed not to come away with anything when we had big chances 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 that tonight, but we just couldn’t overcome it.”