When Liverpool purr like this, delighting in every incisive move and swarming all over panicked opponents, it is hard to contemplate the reality they are a team only marginally closer to the top of the table than they are the bottom three.

This was a performance to showcase all that is thrilling about Jürgen Klopp’s side, from Philippe Coutinho’s invention to Mohamed Salah’s bite, from rare poise at pace in midfield to the relentless press which left Bournemouth gasping for breath. The scoreline may have given the impression of a stroll on the south coast, but everything about the victors was blisteringly energetic.

It was the kind of display to which Klopp will cling in charting a route forward, a standard his team must aspire to reach consistently even if the Premier League title is as good as Manchester City’s already. There are other ways, after all, to make this season a success.

In Coutinho, Liverpool possessed the game’s most compelling performer, the Brazilian operating nominally from the left of a front three and demonstrating all the jaw-dropping attributes which so attracted Barcelona last summer.

Deflecting interest from the hierarchy at the Camp Nou may become the Merseyside club’s principal objective next month, so dazzling was his performance here: there was a free-kick thumped against the woodwork, a whipped assist for the fourth, and an opening goal of such beauty as to set an upbeat tone.

The game was approaching the midway point of the first half, with Bournemouth’s spells in possession only ever fleeting, when Coutinho collected from Ragnar Klavan and exchanged passes with the excellent Andrew Robertson on the flank. The forward used the left-back as a decoy at his side as he drove at the home team’s back-tracking defence, the 25-year-old darting inside Simon Francis, bamboozling Lewis Cook, then finishing sharply inside Asmir Begovic’s near post.

The entire move was played out at breakneck pace. It was his 10th goal of a season that was supposed to have been wrecked by that unfulfilled summer move to La Liga, but there would be regular reminders of his quality on the ball, and the joy he injects into so much of Liverpool’s play.

“It was a nice goal,” Coutinho said through a rather sheepish post-match grin. “Everyone enjoys to play. The manager sometimes changes it, but everyone gives their best and that’s good for Liverpool.”

It was Sadio Mané’s turn to sit out this rout, the Senegalese unused on the bench while Coutinho, Roberto Firmino and Salah had their fun. Opponents are increasingly clued up to the Egyptian’s prowess these days, so impressive has his return to the Premier League proved to date, but few seem capable of nullifying him.

Klopp described Salah’s reward here, with his team’s third just before the interval, as “world class”, as Alex Oxlade‑Chamberlain slid a pass down the right for Salah to collect, cut inside Charlie Daniels and Nathan Aké, and find the far corner with a shot. The skill involved was almost implausible, yet made to look matter-of-fact. That, in itself, is an indication of proper pedigree. The fact Salah already has 20 goals from 26 appearances merely emphasises the point.

In between, the oft-maligned Dejan Lovren had dived in bravely to nod home Firmino’s hook back, Coutinho’s corner having looped up off Georginio Wijnaldum to arc beyond the far post. Daniels might have done better but was frazzled by then, driven to distraction by Salah’s scuttling charges down the flank.

The left-back would soon succumb to a groin strain, joining the hamstrung Josh King in the treatment room, as Eddie Howe surveyed the wreckage of his team’s performance. There is no great disgrace in losing to such livewire opponents, but the meek manner of the surrender alarmed the management.

“We were well off it, flat, and never got going,” Howe said. “We gifted them possession, made unforced errors, and that left us exposed. That was difficult. There have not been many times since I’ve been Bournemouth manager that I’ve felt quite like this after a match.”

Just as telling, perhaps, was his admission the so-called elite teams “are getting better and stronger, quicker than we are”, leaving the likes of Bournemouth, without a win in six games and with trips to Chelsea and Manchester City in the Carabao Cup and league respectively this week, contemplating a difficult winter spent struggling against relegation.

Jermain Defoe did drive against a post from Junior Stanislas’s pass, but it was Liverpool who always carried the threat. Oxlade-Chamberlain, revived in the midfield three, also struck the woodwork before Coutinho’s cross was guided in by Firmino to complete the scoring, allowing Klopp to replace his front three and welcome Adam Lallana’s second cameo of the season.

Liverpool are now 12 games unbeaten in all competitions, which would feel mighty impressive if City were not a speck on the horizon some 18 points away. Regardless, few can live with them when they click. Klopp’s team remain one of the delights of the division.

Romelu Lukaku sets Manchester United on victory path at West Brom Read more