A statement of intent was delivered here, but it was not offered up by Chelsea. Liverpool, for the second season in succession, have prevailed in this corner of south-west London to cast the locals into grisly retrospection and condemn the new regime to their first defeat. Jürgen Klopp’s wild celebrations on the final whistle reflected the psychological significance of this win. These teams are now level on points below Manchester City but, on this evidence, it is the side from Merseyside who have the more realistic aspirations to contend for the title.

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For all that Diego Costa offered the hosts hope of recovery, Klopp’s charges were always the slicker, more coherent team. Their wave of first-half attacks had left Chelsea, a side braced for the onslaught, wounded and wheezing.

There was resilience when required late on to choke any hope of a proper comeback, efforts epitomised by James Milner’s gargantuan display from left-back, even if the management still seemed jittery in the technical area. Liverpool have now claimed seven points from trips to Arsenal, Tottenham Hotspur and Chelsea this season and thumped four past the champions, Leicester City. That renders the defeat at Burnley all the more perplexing but this is clearly a team on the rise.

It is their bite which all-comers will start to fear. Even without Roberto Firmino, who was resting a slight groin complaint, they were irrepressible for long periods up to the break and menacing on the counter-attack once Chelsea had over committed themselves in desperate pursuit of an equaliser. Klopp’s players have already developed that instinctive awareness of each other’s intentions in possession, team-mates darting into space on the gallop to be found with incisive passes. Opponents are beaten as much by speed of thought, though the accuracy and pace of the passing still takes the breath away. “We played football like hell,” said Klopp. Chelsea were simply scorched.

Philippe Coutinho, reintegrated here, is such a pinpoint provider, and Sadio Mané’s aggression and sheer speed across the turf leaves opponents diminished.

Chelsea, with their own rejigged rearguard incorporating the returning David Luiz for the first time, were left dizzied by the rapidity of the attacks. Even N’Golo Kanté could not cope at times and, given his impact for Leicester and Chelsea over 13 months in England, that says it all. “It’s not about ‘intensity’,” said Klopp. “It’s about finding a solution for the opponent. In the first half we had the ball, so it was about movement, playing simple football. The intensity comes when you make a mistake, as we did for their goal, and have to recover. We have to improve but we don’t run like crazy all the time.”

Frenetic, after all, would have implied imprecision.They prospered while the home side dawdled. The struggling Branislav Ivanovic’s crude, albeit unsanctioned, challenge on Georginio Wijnaldum near the touchline earned a free-kick just after the quarter-hour with Coutinho exchanging passes with Milner. Their interplay seemed innocuous enough but it served to disorient a quartet of Chelsea players in the penalty area.

While they ball-watched without an opponent close, only David Luiz and Gary Cahill seemed to sense the danger as three Liverpool players loitered at the far post. Coutinho’s delivery was whipped deliciously over the clutter and, while Daniel Sturridge retreated from an offside position, Dejan Lovren was onside to guide his finish back and across the exposed Thibaut Courtois.

He would be beaten again before the half was out, a throw-in opening up his defence even if Adam Lallana’s touch presented Cahill with the loose ball. Yet the centre-half scuffed his clearance to Jordan Henderson, 25 yards out, whose first touch was magnificent. His second was better, curling a searing shot which dipped beyond the despairing Courtois. This team have kept one clean sheet here in the Premier League all calendar year. “The goals we concede are strange,” bemoaned Antonio Conte after his first defeat as manager. “We must feel the danger and, today, we didn’t. We have to reflect a lot on this match because it is important to understand the situation if we don’t want to repeat another bad season like last year. We don’t feel the danger. Never.”

There was more urgency to their approach after the break as they desperately sought to coax Costa into the game.The Spain forward did well to adjust his body shape and poke a riposte through Milner on the goalline from Nemanja Matic’s cut-back after three Liverpool players overcommitted in the buildup but once Simon Mignolet had thwarted Costa again, the pursuit petered out.

Divock Origi came closest to scoring the evening’s fourth, only for Courtois to summon a fine save, but too many Chelsea players lapsed into the bad habits of last season. Maybe John Terry’s organisational skills were missed but, while David Luiz was hardly at fault, too many others are error-prone or anonymous when it really mattered.

Where Conte had been spared at Watford by his substitutes, the trio of replacements were flung on too late here to make a proper impact with Michy Batshuayi not required at all. The Italian offered his hand to his opposite number at the end but was left waiting forlornly while Klopp celebrated with his players.

Chelsea’s unbeaten record has gone, shattered by the first fellow contender this team have confronted.