Contenders or pretenders? It was a legitimate question to ask of Liverpool given their almost flawless start under Arne Slot and the wait for their first serious Premier League test. Old Trafford does not qualify at present. Chelsea provided it and Liverpool found the answers, hauling themselves back to the summit with a tireless defeat of Enzo Maresca’s emerging team.

New dad Curtis Jones secured victory – Slot’s seventh in eight Premier League matches – moments after Nicolas Jackson had cancelled out Mohamed Salah’s first‑half penalty. Jones was outstanding one week after becoming a father and having slept in the spare room the night before.

The referee, John Brooks, and VAR were also prominent, which is never a good sign. Brooks shattered Slot’s cool touchline demeanour with a perplexing performance, but not the Liverpool head coach’s satisfaction at the most impressive league result of his short reign. He was magnanimous enough to admit the league leaders did not have it all their own way.

Chelsea played with confidence and composure, especially before Salah struck from the spot, and their quality on the ball at Anfield augurs well for the Maresca project. But there was a distinct lack of cutting edge to the visitors. Liverpool recovered from a passive, careless opening to show the resilience, organisation and penetration to strengthen their claims to be potentially the biggest threat to Manchester City’s dominance this season.

Related: Judge Liverpool after next seven games, says delighted Arne Slot

The game could have swung in Liverpool’s favour with six minutes gone when Diogo Jota was hauled to the ground by Tosin Adarabioyo as they pursued Salah’s ball into the Chelsea half. Precedent had been seemingly set 24 hours earlier with William Saliba’s red card for pulling down the Bournemouth striker Evanilson in a similar position. Unlike the Arsenal defender, however, the Chelsea centre-half was shown a yellow card and the decision was backed up by the VAR, Michael Oliver. One difference between the two incidents, and Adarabioyo’s saving grace, was that his defensive colleague, Levi Colwill, was in proximity with plenty of ground available to cover. The colour of the card was not Jota’s only problem. The Liverpool striker took a hefty, accidental blow from the powerful centre-half and spent the next 20 minutes in clear discomfort. He was eventually replaced by Darwin Núñez.

Chelsea escaped again when Cody Gakpo charged down a poor clearance by Robert Sánchez, who was fortunate to see the ball loop back into his arms. But an unconvincing display from the Chelsea goalkeeper was under way. Sánchez’s careless distribution and indecision caused his own team problems throughout. Jones would punish both flaws.

With the influential Alexis Mac Allister rested on the bench after international duty, and because of illness, Jones made his second league start of the season in Liverpool’s midfield. He did more than simply seize the opportunity and minimise the impact of Mac Allister’s absence. He orchestrated Liverpool’s victory.

A two-minute spell midway through the first half encapsulated the midfielder’s telling contribution. First, Jones produced a superb block while on the ground to prevent Cole Palmer converting Noni Madueke’s cross after the Chelsea winger had again beaten Andy Robertson to the byline. Seconds later, with Slot and Anfield raging over Brooks’s refusal to award Salah a penalty following a touch from Colwill, Jones popped up in the opposition area to collect Salah’s deflected cross. The 23-year-old was clearly clipped from behind by Colwill as he shaped to shoot and this time Brooks had no hesitation in pointing to the spot. Salah drilled the penalty home convincingly. Slot allowed himself a little fist pump. Chelsea had their own penalty claim dismissed earlier when Jadon Sancho was caught by Trent Alexander-Arnold.

Jones almost engineered a second goal for a Liverpool team that performed with greater energy and intent once in front. He did brilliantly to dispossess Moisés Caicedo and tee up Salah for a low cross that Gakpo converted at the back post. An offside flag against Salah curtailed those celebrations. In first‑half stoppage time Jones raced on to Núñez’s defence-splitting pass. Sánchez sent the midfielder sprawling, and picked up a booking for protesting against the penalty award that duly followed. Both the penalty and the yellow card were overturned, however, after Brooks checked the pitchside monitor and spotted Sánchez had touched the ball.

Related: Liverpool 2-1 Chelsea: Premier League – live reaction

Liverpool’s VAR frustrations mounted minutes after the restart. Jackson, racing through on to Caicedo’s fine pass, beat Caoimhín Kelleher with a low finish that was disallowed for offside. But a lengthy review found the Chelsea striker had been kept on by Ibrahima Konaté’s toes, prompting a mass sprint to the away end from those in blue when the equaliser was eventually awarded. Their joy lasted less than three minutes.

Salah dissected the Chelsea defence with an exquisite cross from the left. Adarabioyo, Colwill and Sánchez were all caught in freeze-frame. By the time they reacted, it was too late. Jones darted into space to beat Sánchez with a close-range finish. It was his first Premier League goal since New Year’s Day and proved decisive, despite Palmer and Christopher Nkunku, on as a substitute, missing good chances as Chelsea pressed for a second leveller late on.