Liverpool chose the right time to remind Europe why they reign supreme in the Champions League. The pressure was on in Salzburg and Jürgen Klopp’s team responded with a performance befitting European champions to preserve their dreams of a third consecutive final appearance and a return to Istanbul. It was far from easy against the Austrian champions. Liverpool made it appear so.

The Premier League leaders claimed first place in Group E with a victory built on the experience of champions, resolute defending and brilliant execution from their front line. Salzburg contributed to an enthralling finale but from the moment Sadio Mané created the breakthrough for Naby Keïta the visitors assumed absolute control. Mohamed Salah, guilty of several earlier misses, struck an exquisite second 100 seconds later and Klopp’s team cruised into the knockout phase they thrive upon. Liverpool have reached the final of every European competition they have played in under Klopp, never losing a two-legged European tie with him. They can head to the Club World Cup in Qatar next week confident of continuing those remarkable sequences when the Champions League resumes in the new year.

Victory looked routine by the time Mané missed Liverpool’s final chance of the night but it had been a tense affair until Keïta struck. Alisson and Virgil van Dijk had to be at their authoritative best as Jesse Marsch’s team started with the belief they could qualify with Napoli at the expense of the European champions. Salzburg’s coach and players had been full of confidence in the buildup to the club’s biggest European night. It was immediately apparent they had tools to back up the talk. From the bravery to play through and around Liverpool’s press to intricate one-touch moves around the visitors’ penalty area, the hosts opened with the arrogance of youth and the belief of domestic champions. Van Dijk was called into evasive action to deny both Erling Haaland and Hwang Hee-chan inside the first minute. Notice had been served that this was to be a demanding night for the Liverpool defence. Notice was taken.

Naby Keïta enjoyed a productive night against his former club. Photograph: Lukas Barth/EPA

Alisson made six saves in the first half – only one in the second – with the most impressive arriving when the Salzburg playmaker Takumi Minamino back-heeled Hwang into space and he looked to score from close range, having twisted inside Jordan Henderson. The Brazilian made a fine left-handed stop and also denied the eye-catching Enock Mwepu twice, Hwang again and Haaland before the break. The contest was utterly compelling because it flowed end to end and, despite Salzburg’s swagger in possession, it was Liverpool who crafted the clearer openings. Fine goalkeeping from Cican Stankovic and poor finishing by Salah ensured Liverpool were kept waiting for the breakthrough.

The game opened at a frenetic pace with more goalmouth activity in the first 15 minutes than the entirety of many contests. Liverpool’s first excellent opening arrived from the direct source of a Dejan Lovren ball down the centre. The Salzburg central defender Maximilian Wöber, a weak link, misjudged the flight and allowed Salah a clean run on goal. The Egypt international took the shot early but Stankovic stood up well to make an important block.

Salah had no excuse for failing to beat the goalkeeper next time, however. Keïta burst into space vacated by Wöber after the Austrian overcommitted. As Salzburg defenders closed in the Guinean released Salah free inside the area but, with only Stankovic to beat, he dragged a first-time shot horribly wide.

The Liverpool forward almost made amends on the stroke of half-time with a delightful pass into the overlapping run of Keïta. Stankovic was again to the rescue, racing out quickly to smother the midfielder’s shot and breathing a sigh of relief when the rebound struck Keïta’s chest and sailed out for a goal-kick.

Erling Braut Haaland reacts with fury after missing a chance. Photograph: John Sibley/Action Images via Reuters

It was the same story at the start of the second half. The former Salzburg striker Mané released Salah in behind the defence with an exquisite pass but his instinctive shot sailed over. When Roberto Firmino threaded another ball between the hosts’ defence and Salah attempted to round Stankovic, the keeper got a vital touch at the last and another chance had gone.

It was a mark of champions that this did not disturb Liverpool or Salah. Two goals in two minutes, both involving Stankovic rushing from his line unnecessarily and excellent finishes, turned a troublesome night into a triumphant one for Klopp’s team.

The Salzburg keeper may have been over-confident following earlier events but beyond question was the quality of Liverpool’s goals. The opener arrived moments after Joe Gomez had replaced the injured Lovren. Trent Alexander-Arnold swept the substitute’s pass over to Andy Robertson, who touched on to Mané. In a flash the Senegal international darted past Jérôme Onguéné into the area and, as Stankovic stormed off his line, he clipped an inch-perfect cross from the left for Keïta to head home.

Salzburg’s hopes crumbled within seconds. Henderson sprayed a hopeful ball behind Onguéné for Salah to chase. The defender connected with a weak header and the error was compounded by Stankovic sprinting out of his area in an attempt to clear. Salah easily beat him too it but his first touch took the ball towards the byline. No matter. He simply curled a deft finish goalwards and forgot the previous misses as his hardest chance of the night nestled inside the far post. An outstanding finish and Liverpool coasted into the knockout stage from that point on. They remain the team to fear in Europe.