This devastating Liverpool machine will take some stopping. For the second successive year Jürgen Klopp’s side will sit top of the tree at Christmas after chewing up and spitting out another innocent opponent to move 11 points clear at the Premier League summit. After being overthrown by Manchester City last season the challenge for a Liverpool team juggling five competitions and a marathon festive period is simply to stay put. In eight of the past 11 seasons the leaders on Christmas Day have gone on to clinch the title but Liverpool, eerily, have been the exception on each of those three occasions.

An irresistible performance by a reinvigorated Mohamed Salah, who Klopp declared is again firing at 100%, proved the catalyst as Liverpool extended their unbeaten league record to 33 games. Naby Keïta doubled their advantage following a cool Alex Oxlade-Chamberlain opener before Salah completed the scoring as Liverpool swept aside Bournemouth, who struggled to lay a glove on them. Liverpool queued up in search of a fourth goal but for Klopp the most pleasing takeaways were not needing to call on Sadio Mané and a first clean sheet in 14 matches.

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“I forgot actually how it feels,” said Klopp beaming. “That was the most used word when I came in the dressing room: ‘Clean sheet, clean sheet, clean sheet.’ Obviously everybody was desperate for that and now we have it, so let’s have it more often. The next game where a clean sheet would be useful is already around the corner, against Salzburg on Tuesday.”

With one eye on that match – Liverpool must avoid defeat to guarantee qualification to the Champions League knockout stages – Klopp again rotated and made seven changes but they beat Bournemouth with such ease that he was able to hand the teenager Curtis Jones his league debut. After giving Salah, Jordan Henderson and Roberto Firmino a breather in midweek, this time Klopp left Mané and Trent Alexander-Arnold on the bench, although the latter replaced Dejan Lovren five minutes before half-time. By that point Liverpool had established a two-goal lead after Bournemouth unravelled following an injury to Nathan Aké.

Bournemouth are teetering above the relegation zone after a fifth consecutive defeat and a galling afternoon was compounded by injuries to Aké and Callum Wilson, with both clutching their hamstrings as they departed prematurely. Harry Wilson, ineligible to face his parent club, looked on from the stands alongside Bournemouth’s walking wounded, with Eddie Howe’s injury list mounting at the worst possible time. “It’s probably the biggest challenge we’ve ever faced since we came into the Premier League,” Howe said. “The game seemed to hinge on Nathan’s injury. It was a hammer blow, a double-whammy with the injury and the goal and we never recovered.”

With this the first of five games in 11 days Liverpool initially appeared to pace themselves, patiently probing in search of an incisive opening –and when Aké was withdrawn 10 minutes before the interval, Bournemouth were unsettled and the visitors unleashed their killer instinct. Henderson played a wonderful raking ball downfield in search of Oxlade-Chamberlain, who easily eluded Chris Mepham and prodded beyond Aaron Ramsdale.

Without Aké, Bournemouth’s back line was always susceptible to further damage. Firmino almost applied the finishing touches to an Alexander-Arnold cross, before an exquisite backheel by Salah freed Keïta to score his first goal of the season. A swell of supporters gasped as Salah flicked the ball into the path of the midfielder, who rounded off an effortless give-and-go by poking home, and the match soon descended into a harrowing game of defence versus attack.

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Alexander-Arnold continued to pierce holes down the Bournemouth left as Liverpool toyed with their opponents and it seemed only a matter of time before Salah, who had twice gone close, got in on the act. When Aké’s replacement, Jack Simpson, gave the ball to Keïta, Liverpool sensed blood and their next move seemed almost inevitable. Keïta slid in a weighted pass for Salah, who raced in behind Mepham before squeezing the ball into the far corner. “It was an absolutely super performance,” Klopp said. “The team performance was really mature and professional – just what we needed.”