Sadio Mané announced his return to full fitness, and Liverpool their readiness for the Champions League play-offs, as Jürgen Klopp’s side recorded a convincing win over Bayern Munich in the Audi Cup. “Nothing against Crystal Palace, Leicester City or Hertha Berlin,” said Klopp ahead of Tuesday’s friendly: “But this is the next level and I think we are ready.” He thought right.

The Senegal international scored one and created one as Liverpool’s formidable attacking range overwhelmed the Bundesliga champions on home soil. Daniel Sturridge added an outstanding third before limping off with what appeared a thigh injury sustained in the act of scooping the ball over Bayern goalkeeper Sven Ulreich.

Mané is still working up to full speed from the knee ligament injury that curtailed his last campaign on 1 April and had looked inevitably rusty in the win in Berlin on Saturday. In Munich, however, he was sharp, fast and punishing. As all of Liverpool’s forwards were. Mohamed Salah and substitute Sturridge completed a hugely encouraging night for Klopp ahead of Friday’s draw for the Champions League play-off stage.

Bayern started brightly but could not live with Liverpool’s devastating pace and penetration on the counterattack. Klopp’s team struck from their first foray forward, created entirely by Roberto Firmino who dispossessed Corentin Tolisso in central midfield and played a perfectly weighted pass behind Javier Martínez into the path of Mané. The striker, switched to the left to accommodate new signing Salah, took one touch before beating Ulreich with a convincing finish.

Salah almost made it two moments later when connecting with Alberto Moreno’s excellent low cross from the left but Ulreich saved smartly at the back post. The Bayern keeper, standing in for the injured Manuel Neuer, also saved well when Moreno swept a free-kick from 20 yards towards his top corner. Liverpool’s out-of-favour left-back, it must be said, enjoyed a fine evening as he and Mané terrorised Rafinha at right-back.

Although the hosts controlled much of the play they rarely threatened to break down Liverpool’s compact and disciplined defensive shape. That, as much as anything else on display at the Allianz Arena, bodes well for the coming season with Klopp stating Liverpool’s overall defending must improve.

The Liverpool manager did not restrain his celebrations when Salah extended the advantage on 35 minutes. Klopp’s delight stemmed from the quality of the build-up and with good reason. Mané held the ball up on the left of the penalty area, teasing Rafinha all the while, before releasing Moreno to the by-line with a delightful flick of the instep. The Spanish left-back’s low cross took a slight deflection and found Liverpool’s £36.9m record signing unmarked at the back post where he headed over the line from close range.

Bayern looked a bewildered and despondent side after Liverpool’s second goal. Carlo Ancelotti’s team face their first competitive match of the season on Saturday – the German Supercup Final against Klopp’s old club Borussia Dortmund – and their preparations have been far from ideal. The Bundesliga champions have lost to Arsenal, Milan, Internazionale and now Liverpool in pre-season. Robert Lewandowski’s obvious displeasure at the poor quality service he received was perhaps another indication of an unhappy Bayern camp.

The Liverpool fans in Munich indulged in a series of “Olés” in the second half as their team prospered in possession. Mané had departed at the interval, enabling Philippe Coutinho to move forward from the left-sided midfield role from where he delivered quick, accurate and telling balls into the front three in the first half. Firmino’s intelligence on the ball and awareness of those around him was also instrumental in Liverpool’s impact in the final third.

Sturridge sealed Liverpool’s victory with five minutes remaining when he raced on to a delightful through ball from fellow substitute Ben Woodburn and lofted a glorious chip over Ulreich. In doing so, however, he appeared to suffer a thigh injury and was swiftly replaced by Dominic Solanke. The one sour note on Liverpool’s night.

Klopp’s team will now play Atlético Madrid in Wednesday’s final after Diego Simeone’s team beat Napoli in a feisty encounter earlier in the evening. Jose Callejon swept the Italians ahead before Fernando Torres scored past his former Liverpool team-mate Pepe Reina and Luciano Vietto made it 2-1. Atlético defender Diego Godín was sent off late on for a second bookable offence that sparked angry exchanges between the two benches.