Liverpool have won at Arsenal and Chelsea already this season

Liverpool manager Jurgen Klopp was bear-hugging and chest-bumping his triumphant players as Chelsea counterpart Antonio Conte was back in the dressing room contemplating a defeat about which he could have no complaints.

A Premier League collision between two of Europe's A-list coaches ended in a 2-1 win for Klopp's Liverpool that was far more comfortable and convincing than the Stamford Bridge scoreline suggests.

Conte, in contrast, suffered his first loss since taking over at Chelsea to complete an indifferent week after they had to battle to get a point at Swansea City last Sunday.

So what are the early lessons for Klopp and Conte as Liverpool's season continues to gather pace and Chelsea's suffers a setback?

Klopp's threat to big guns

Klopp made his intentions clear with a bold claim when Liverpool opened their new Main Stand at Anfield recently.

"We want to go to the best teams in the world and give them hell," said Klopp as his managerial mission statement - and he has made good on his promise on the domestic front at least.

Liverpool's three trips to London this season have yielded seven points from this win at Chelsea, with a 4-3 victory at Arsenal and a 1-1 draw at Tottenham that should have brought the maximum return.

While it may be stretching the point to call this a hellish experience for Chelsea, it was certainly uncomfortable from first to last on a night when much of the early-season optimism around the new Conte regime was suddenly tempered by a heavy dose of realism.

Liverpool's win should have come as no surprise given the manner in which they have performed against the teams that are widely accepted as the Premier League's most powerful since Klopp was appointed manager.

In 14 games against Arsenal, Chelsea, Manchester United, Manchester City and Spurs since arriving at Liverpool almost a year ago, Klopp has lost only twice. He suffered a 1-0 home defeat by Manchester United in January and lost the League Cup final on penalties to Manchester City at Wembley in February.

The sequence has included a 3-1 win at Stamford Bridge and a 4-1 triumph at Manchester City last season - as well as victory over two legs against Manchester United in the Europa League, which included a 2-0 win at Anfield and a 1-1 draw at Old Trafford.

The only flaw in Klopp's masterplan is when Liverpool throw in the sort of dismal performance that saw them deservedly lose 2-0 at Burnley this season.

This latest win at Chelsea was Klopp and Liverpool putting down another marker that they are more than capable of competing with the best - and if they can put things right against the rest then their growing momentum will become even more ominous.

Jurgen Klopp praises 'brilliant' start as Liverpool beat Chelsea

Riverdance and fist pumps - touchline watch

The meeting between Conte and Klopp did not just carry heavy Premier League significance - it was a game where eyes were trained on the technical area as well as on the pitch.

Conte and Klopp are two of the game's most charismatic and animated managers, so it was always going to be an eventful evening for fourth official Bobby Madley.

Madley crossed swords with both, delivering an early warning to Conte for straying outside his designated area as well as being in regular conversation with Klopp.

Italian Conte prowled his technical area throughout, dark-suited and with shiny back shoes glinting in the floodlights. Klopp opted for a black Liverpool tracksuit.

Antonio Conte (right) lost his first home league game as a manager since January 2013, ending a run of 30 games without defeat

In what might have been a sign of how the early phases were developing, Conte was all agitated, nervous action, while it took Klopp until the 13th minute to even leave his seat - and that was only to offer up a minor tweak at a Liverpool corner.

The real Klopp was unleashed when Jordan Henderson's magnificent 25-yard strike curved and dipped beyond Chelsea keeper Thibaut Courtois after 36 minutes.

Klopp leapt from his dugout with the exclamation "boom" as the shot flew in and Liverpool took control. It was a control they never seriously threatened to relinquish.

The goal may even be part of Klopp's wider plan because, since he took charge, Liverpool have scored 15 Premier League goals from outside the box, five more than any other side in that time.

The German was, however, furious at the manner in which his defenders, Joel Matip in particular, went to ground far too easily and allowed Nemanja Matic to set up Diego Costa's goal that gave Chelsea brief, albeit unfulfilled, second-half hope.

There was an air of increasing desperation about Conte, including one impromptu "Riverdance" jump on the spot when a decision went against Chelsea.

In the end he was as subdued as his Chelsea side and at the final whistle it was Klopp who embraced his Liverpool backroom staff before going around all of his players, back-slapping, bear-hugging and chest-beating before pumping his fists in the direction of their fans.

On this night, Klopp overcame Conte on all levels.

We must be focused - Antonio Conte

Klopp wins tactical battle

Klopp's tried and trusted "gegenpressing" style external-link and the pace provided by the likes of Daniel Sturridge and new £34m forward Sadio Mane appeared to leave Chelsea overcome with caution from the kick-off.

Conte's side, missing the influence and direction of injured captain John Terry, simply sat too deep and did too little, especially in the first half. It was an invitation to assume superiority that Liverpool, tactically progressive and proactive under Klopp, were never going to pass up.

Liverpool looked mobile, competitive, quick and fluent. Conte's Chelsea were laboured and lacking guile, with Matic and Branislav Ivanovic in particular looking like two players close to outliving their usefulness at Stamford Bridge.

The important Roberto Firmino was out with a groin injury but Klopp utilised a front three of Sturridge, Mane and Philippe Coutinho in a manner that compensated for the Brazilian's absence.

Chelsea have not kept a clean sheet in the past seven home Premier League games against Liverpool

David Luiz looked exactly the same player that left Stamford Bridge for Paris St-Germain two years ago, although blame for this defeat could certainly not be apportioned to him.

Klopp's substitutions were more structured and logical than Conte's. Divock Origi came on to replace Sturridge just before the hour as the striker appeared to pick up a knock, while the tiring Coutinho was replaced with the more defensive-minded Lucas to lock down the 2-1 result with eight minutes left.

Conte, surprisingly, waited to make changes even after Costa, who spent the night isolated and toiling alone, pulled one back after 61 minutes. Chelsea failed to cash in on that rare moment of supremacy.

In the end, it was the 83rd minute before Conte made a change, with the odd voice in the stands having demanded them earlier - and then he made all three at once.

Cesc Fabregas was belatedly introduced for Matic, while Victor Moses and Pedro replaced Willian and Oscar. The big surprise was that £33m summer signing Michy Batshuayi remained unused as Chelsea chased a goal.

Conte has not made a substitution in the Premier League before the 71st minute this season - Moses at Watford - so he is clearly not a natural exponent of the early change.

In Conte's defence, though, his substitutions have generally been positive and helped get late wins against West Ham and particularly at Watford, where Batshuayi scored an equaliser and fellow sub Fabregas set up Costa's winner.

Here, though, Klopp's Liverpool were more organised and seemed more tactically aware of what their gameplan was.

How far can Liverpool go?

Liverpool have won five of their past nine Premier League games at Stamford Bridge

As Liverpool's team coach pulled out of west London and headed back to Merseyside before midnight, it would have been accompanied by a growing sense of confidence, even excitement, about their prospects this season.

The loss at Burnley will act as the check on over-optimism, but Liverpool and Klopp can take great encouragement from Friday's win, as well as those performances at Arsenal and Spurs and the 4-1 dismissal of champions Leicester City at Anfield.

Matip, with the same languid gait and build of the young Rio Ferdinand, has started solidly in central defence and was given few problems by the poorly served Costa, while Dejan Lovren grows in stature alongside the free transfer from German side Schalke.

Klopp's big summer buys have also settled well. Georginio Wijnaldum was a solid, steady presence and the pace, verve and tireless running of Mane gives Liverpool the sort of defending from the front and menace they have lacked since the departure of Luis Suarez - although it should be stressed this is not to compare the two in terms of quality.

Liverpool's players clearly have faith in Klopp and the bond was shown by the warmth of the embraces between team and manager at the final whistle.

This has been - Burnley apart - a highly impressive start by Liverpool. It is too early to talk in title terms but they have no reason not to already set their sights on a place in the top four.

As Klopp also said when that imposing new stand was opened: "If there is one part of life where you can challenge the best in the world then it's football. It depends on your attitude.

"If always the people with the best circumstances would win, this world would be an ugly place. We all have the chance to fight for everything. It's not about having a guarantee; it's about having the opportunity."

Arsenal, Spurs and Chelsea will do the same. So why not Liverpool after emerging unscathed, and with seven points, from those three trips to the capital?