Jürgen Klopp has rebuilt a ­formidable Liverpool unit with less time and money than Chelsea took to ­squander £1bn on a collection of individuals under Todd Boehly. Contrasting approaches and rewards collided at Anfield where a homegrown 20‑year‑old full‑back, Conor Bradley, dismantled Mauricio Pochettino’s strangers on a statement night for the Premier League leaders.

Bradley was inspired, the Kop ­singing his name throughout, as Klopp’s team toyed with their ­Carabao Cup final opponents a month before their Wembley date. Liverpool can count down the days until they meet again. Chelsea will be already dreading the reunion.

Related: ‘Better than us in all areas’: Pochettino bemoans Chelsea display at Anfield

The visitors were angered by the referee Paul ­Tierney’s failure to award them two penalties – Liverpool had no complaints with Klopp’s bete noire for a change – but the simple truth is they were outfought, outmanoeuvred and outclassed all night.

“They were better than us from the first action,” Pochettino said. “They were better than us in all areas.”

Klopp’s faith in the Liverpool squad he will leave behind was vindicated once again in a high-octane, high-calibre per­formance. They refused to allow Chelsea time to play through a ­relentless press and peppered Djordje Petrovic’s goal almost on sight. Bradley became the first Northern Ireland international to score for the club since Sammy Smyth 70 years ago and he took his assist tally to five in four games. Darwin Núñez struck the woodwork four times, once from a penalty, and took 11 shots at goal without scoring. Chelsea won their first corner in stoppage time.

Klopp’s decision to retain ­Bradley in place of the fit-again Trent ­Alexander-Arnold was another example of his managerial shrewdness. It was a huge show of faith that elevated the young defender’s game beyond the heights he reached during the deputy captain’s recent absence.

Bradley began a superb night’s work when crafting the first chance for Núñez, a man on a mission to score from anywhere, but Petrovic read the striker’s attempted lob.

Petrovic alone kept the first‑half scoreline semi‑respectable. He tipped another Núñez first‑time effort, a blast from Alexis ­Mac ­Allister’s threaded pass, on to his crossbar and a left‑foot drive from the Uruguay international on to a post. He denied Liverpool again when tipping away a daisy-cutter from Curtis Jones. But the visiting keeper was let down badly by his central defenders when the hosts inevitably took the lead.

Ben Chilwell was also at fault when losing the ball weakly to Bradley. The defender swapped passes with Jones and found Diogo Jota in space outside the Chelsea area. The striker weaved between non-existent challenges from Thiago Silva and Benoît ­Badiashile – John Terry, watching from the away end, must have been sickened – and poked a close‑range finish beyond Petrovic. The goal stood following a VAR review for a possible handball by Jota when Silva struck a clearance against him.

Chelsea had their first penalty appeal dismissed when Conor ­Gallagher went down under a challenge from Virgil van Dijk. There was contact from the Liverpool captain’s arm and knee but Gallagher collapsed far too easily.

Liverpool extended their lead courtesy of their marauding right‑back’s first goal for the club. Luis Díaz spun away from Enzo Fernández to send Bradley sprinting clear down the right. The youngster showed excellent composure to sweep a low finish beyond Petrovic and inside the far corner. VAR again stalled Anfield’s celebrations as it reviewed a ­possible foul in the build-up by Jota on Chilwell, who argued he would have occupied Bradley’s space otherwise, before allowing the goalscorer to savour his moment after all.

It should have been three before the break. Tierney ruled in Liverpool’s favour again when ­Badiashile stood on Jota’s foot inside the area. The ­referee had no hesitation in pointing to the spot but Núñez struck a post with Petrovic diving the ­opposite way.

Pochettino made his feelings clear on Chelsea’s anaemic first half. The manager made three substitutions at the interval and should have been rewarded immediately when one, Malo Gusto, broke clear and centred for another, Mykhailo Mudryk. Unmarked and 10 yards out, Mudryk skied high into the Anfield Road stand.

Bradley’s evening went from strength to strength. He made it five assists in four outings when ­receiving Van Dijk’s cross-field ball and ­sprinting clear of Badiashile, now shifted out to left-back in place of Chilwell. At full pelt he delivered a perfect cross into the penalty area and Dominik Szoboszlai soared above the Chelsea defence to head home.

Christopher Nkunku injected much-needed ­menace into the Chelsea attack and pulled a goal back when steering Carney Chukwuemeka’s ball into the bottom corner. He also had a penalty claim rejected after a kick in the heel from Van Dijk. Núñez hit the woodwork yet again with a thumping header from an Andy Robertson cross before setting up the fourth for Díaz with an ­inviting cross to the back post. Liverpool are on a roll heading into their encounter with Arsenal on Sunday.