The pre-match instruction had been pretty simple from Jürgen Klopp following defeat in Naples. “We have to show that we still know how it goes,” he advised. Back to emphatic victories in the Champions League, back on top of the group and Mohamed Salah back among the goals and records too; Liverpool do not forget that easily.

Salah struck twice in a convincing defeat of Red Star Belgrade to bring up a half century of Liverpool goals quicker than any player in the club’s illustrious history. Albert Stubbins, the previous fastest, needed 77 games to get his 50. Salah just 65. What other forwards would give to struggle as the Egypt international has done in a season that has yielded six goals so far with the guarantee of many more to come. Roberto Firmino and Sadio Mané were also on the scoresheet for the first time in seven and eight club games respectively as Liverpool’s front three clicked on the European stage.

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It would have been more had Mané converted a second-half penalty or Adam Lallana finished when through on goal. Not that Liverpool were complaining.

Napoli’s 2-2 draw at Paris Saint-Germain ensured victory took them to the top of Group C with the return at Red Star next. Klopp took comfort in more than the scoreline.

Fabinho impressed in the heart of Liverpool’s midfield after an uncertain start and Xherdan Shaqiri’s instinctive creativity helped break Red Star’s shape and their discipline. Joe Gomez was also outstanding alongside Virgil van Dijk in central defence as the Serbian champions endured another bruising European away defeat. Their previous outing was a 6-1 defeat at PSG that is under investigation by French police amid allegations of match-fixing. They are allegations that Red Star vehemently deny.

Of more immediate concern at Anfield was the thankless task of trying to contain Liverpool without encouragement from their vociferous supporters. Officially, at least. Uefa had banned Red Star from selling tickets to their first two away matches in the group stage following a pitch invasion following the play-off win against RB Salzburg.

Pockets of Serbian voices could be heard around the ground throughout the game, however. They would have been misled by the 20 minutes that preceded Firmino’s opener. Red Star looked comfortable and threatened in numbers. They should have taken the lead when Lorenzo Ebecilio’s corner found Srdan Babic unmarked in the penalty area but, with the home defence static, the centre-half volleyed over.

Facebook Twitter Pinterest Roberto Firmino opens the scoring for Liverpool. Photograph: Michael Regan/Getty Images

Liverpool needed time to find sharpness in their passing and movement. A change in personnel and formation from Klopp may have been a contributing factor. The hosts started with Salah at the spearhead of their attack with Mané, playing with his broken thumb in a protective cast, Firmino and Shaqiri roving behind. There was also a rare start for Fabinho with Jordan Henderson and Naby Keïta sidelined by hamstring injuries.

Fabinho grew in tandem with the confidence in Liverpool’s performance. The Brazil international was caught waiting for possession twice in the first half but otherwise settled comfortably on only his second start since a £43.7m summer switch from Monaco. His distribution, strength and energy in central midfield made for an encouraging contribution, although it was the quartet in front of him who truly stood out with their flicks, back-heels and mesmerising link-up play.

The breakthrough was pristine in its creation and execution. Shaqiri was the instigator, as was the case for Salah’s winner at Huddersfield on Saturday, releasing Andy Robertson down the left with a perfectly weighted pass behind the right-back Filip Stojkovic. Robertson provided a wonderful cutback from the byline into the run from deep of Firmino. Liverpool’s No 9 took one touch inside Nenad Krsticic before driving his 14th Champions League goal for the club down the centre of Milan Borjan’s exposed goal.

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The opening goal invigorated Liverpool’s display. Firmino almost released Mané with an exquisite flick seconds after his opener and Robertson sliced a good chance wide following a flowing move between Shaqiri, Salah and the Senegal international. A second seemed only a matter of time, and it arrived on the cusp of half-time with Shaqiri involved once again. Georginio Wijnaldum threaded a fine ball into the Switzerland international and his deft touch released Salah free on the right of the area. The Egyptian drove an unstoppable finish beyond Borjan.

Salah’s second of the night stemmed from a more questionable source early in the second half. The referee Daniel Siebert was initially unmoved by half-hearted penalty claims when Mané went to ground attempting to get on the outside of Stojkovic. His additional assistant on the far side of the Kop goal identified an arm from the Red Star captain catching the striker at throat-height. Siebert eventually pointed to the spot and, while the visitors raged at a decision that was hardly a game-changer, Salah lined up a penalty that was swept emphatically down the middle of Borjan’s goal. His half century of Liverpool goals was also his 14th in the Champions League.

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Mané missed the opportunity to follow Salah’s lead from the spot when, after Lorenzo Ebecilio headed a free-kick against his own arm inside the area, Borjan tipped his penalty superbly on to the crossbar. Mané was unable to convert the rebound but moments later, after substitute Daniel Sturridge had released him inside the area, the striker prodded beyond the keeper from close range to complete Liverpool’s comfortable night.