The Brentford fans ought to have known better. After all, Darwin Núñez had scored a fabulous goal against their team in the corresponding fixture last season. Still, when the centre-forward entered as a 65th-minute substitute, they were ready with their taunt, one that compared him unfavourably with his Liverpool predecessor, Andy Carroll.

Núñez had travelled to London having scored four times all season. The scrutiny burned. It is no kind of return for an £85m record signing. Arne Slot had insisted he would come good, that it was simply a matter of getting him into the right spaces and situations against deep-set opponents. How it would do so at the very last.

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The initial signs were not good. Núñez misdirected a decent headed chance. He would send a blast into the stands. Liverpool threatened throughout. They dominated in pretty much every area, every metric. But when the board went up to show four additional minutes, they had failed to find the breakthrough with 35 shots.

Finally, they got one to work and Núñez’s delight knew no bounds, the celebrations wild. Another substitute, Harvey Elliott, had sparked the move up the inside-right and when Trent Alexander-Arnold got a kind ricochet off Yehor Yarmoliuk, he tried again, crossing low and there was Núñez to sweep home.

There would be more. It again involved Elliott and was again a Núñez conversion; this one lashed high into the net. His goal here in last season’s 4-1 win had been a lifted finish after a quick break. This was all about the power. It was emphatic, never in doubt, defined by a sense of liberation. “You’re just a shit Andy Carroll,” went the chant. Now it was delivered by the travelling supporters, tongues in cheeks.

Liverpool needed this after draws against Manchester United and Nottingham Forest; after dropping points in four of their previous seven Premier League games. Slot was particularly frustrated by his team’s inability to make the difference in front of goal against United and Forest; in the Carabao Cup semi-final, first-leg defeat at Tottenham, too.

Look at the xG stats, he said post-match. They support the argument that there has not been too much wrong with the performances. Liverpool just needed something to click. Núñez made it happen.

This was a victory built on firm foundations; on the pace and physical dominance of Virgil van Dijk and Ibrahima Konaté in central defence. On the physicality throughout the team, really. It served not only to embellish the division’s best away record; the only unbeaten one. It was Liverpool again throwing down the gauntlet to their title challengers.

Related: Arne Slot rewarded for patience as Liverpool keep calm and carry on | Barney Ronay

It was a slow-burn contest, Slot watching and waiting at the outset, trying to figure Brentford out. They were difficult to classify in terms of formation, plenty of shifting parts. Bryan Mbeumo had the licence to roam off the right wing. Mikkel Damsgaard embraced his No 10 role.

Brentford flickered. Damsgaard could not react early on to tap home a deflected Mads Roerslev cross; was Roerslev offside? Christian Nørgaard sent a header wide from an Mbeumo free-kick. You know what Mbeumo wants to do – cut inside and unload. He tried that on several occasions.

It was Liverpool who settled into their patterns, stretching Brentford, asking the questions. Their most eye-catching moment of the first period came on 35 minutes when Dominik Szoboszlai took a touch and rattled the crossbar with a fizzing drive from 25 yards.

Liverpool had their regrets. Szoboszlai had started to move into dangerous areas by that point. Twice he quickened the pulse only to lack the finish, the second after a mazy dribble.

It felt as though Liverpool were going to break the game open before half-time, especially when Cody Gakpo sparked a quick transition and did not stop to admire the pass. Szoboszlai found Mohamed Salah, who went back across for Gakpo but his final action was neither a dinked finish nor a pass.

Earlier, Luis Díaz, who played as a false 9, could not execute a slightly awkward header from Konaté’s floated cross, Díaz’s contact was off his shoulder. Ryan Gravenberch had also worked Mark Flekken from distance.

Liverpool’s control became pronounced. Brentford are comfortably the league’s highest scorers at home with 29 goals from their 12 games but Thomas Frank’s idea for all-out attack was overtaken by the need to maintain a defensive shape.

Díaz would see a low shot turned away by Flekken before Núñez started with misses. The game became a little more open after Alexis Mac Allister had headed into the side-netting. Brentford had a few moments, mainly Mbeumo-inspired. Yoane Wissa would trouble .

Liverpool continued to push, they continued to shoot. Alexander-Arnold fizzed one past a post. Salah did the same. Núñez tore through the frustration and he would even get away with a bad tackle on Nathan Collins that had Slot wincing. It was indisputably Darwin’s day.