With the exception of José Mourinho’s stifling tactics it had always seemed a question of when, not if, Liverpool would polish their performances with a killer touch. The answer arrived in emphatic style here in Slovenia, where Jürgen Klopp’s side ignited their Champions League campaign with the biggest away win in Liverpool’s rich European history.

One win in eight games before this trip had tested Klopp’s humour but not his conviction that Liverpool are “on a good way”. Seven unanswered goals on the road in the Champions League reaffirmed the belief of manager and players. Roberto Firmino and Mohamed Salah scored twice while Philippe Coutinho, Alex Oxlade-Chamberlain, with his first Liverpool goal, and Trent Alexander-Arnold were also on the scoresheet as the visitors secured the lead in their group.

“I didn’t know about the record until after the game,” the Liverpool manager said. “The wonderful history of this club can feel like a backpack at times, so it is nice to write our own good piece of the history. It will be difficult to beat that record.

“It is quite rare to win 7-0 but it showed we did unbelievably well. The boys deserved that. When you don’t score it is a challenge to stay confident but we will try to use this result now.”

Liverpool’s impatience for a first win in the group stage was undisguised. It was evident in Klopp’s pre-match press conference when he spoke of making amends for the points dropped against Sevilla and Spartak Moscow. It was clear in a team selection that showed no sign of complacency against the Slovenian champions, the lowest ranked team in the group, as the Liverpool manager fielded the same attack who faced Manchester United on Saturday. And it was demonstrated in a commanding, clinical performance that overwhelmed Maribor from the first whistle

asthe perfect way to release the frustrations of the dour United stalemate and the perfect opponents, it has to be said. The hosts had no answer to Liverpool’s movement, strength and quality and were swiftly routed.

Roberto Firmino puts Liverpool ahead in the fourth minute of the match. Photograph: MB Media/Getty Images

Firmino started the torment for Maribor by tucking home his first goal in six games in the fourth minute. The Brazil international had forgotten his security pass on the way into the stadium and was sent back to the team bus to retrieve it by a sharp-eyed steward, but he had no problem locating weaknesses in the home side’s defence. Salah and Coutinho enjoyed similar success against a regularly exposed rearguard, and it was the hero of Egypt who instigated the breakthrough when he broke away from Marko Suler’s lunging challenge on the right wing. Salah sprinted on, picked out Firmino unmarked in the centre and the forward converted from close range.

Number two followed quickly and this time Firmino was the instigator. He spun away from his marker in the centre circle and found Salah with a fine cross-field ball. Salah fed James Milner, recalled on the right of the midfield three with Jordan Henderson rested, and he crossed for Coutinho to sweep a first-time finish beyond Jasmin Handanovic from 12 yards. Milner has found opportunities limited this season but he seized it here, driving at Maribor and providing an accurate range of passes throughout.

Firmino created the third, too, returning the favour for Salah, whom he released behind the defence with a perfectly weighted ball, having ridden several challenges in the buildup. Liverpool’s summer signing beat the advancing Handanovic with a measured, angled finish and the visitors were home and hosed with 70 minutes left to play. But there was no let-up in their work rate or adventure.

The combination of Coutinho’s craft and Alberto Moreno’s pace on the left troubled Maribor regularly, the full-back striking the side netting from one chance created by the playmaker, and it was that source that provided Liverpool with their fourth. Moreno crossed hard and low from the byline, having been released by Coutinho, and there was Salah to tap into an unprotected net.

Maribor have conceded four goals in 10 domestic home fixtures this season but they continued to be ravaged by Liverpool en route to their heaviest European defeat. Firmino scored his second when he met Coutinho’s free-kick with a glancing header that sailed across Handanovic and inside the far post. Firmino and Salah departed to well-earned ovations from the travelling Liverpool supporters, and it seemed almost cruel of Klopp to introduce Oxlade-Chamberlain and Daniel Sturridge from the bench.

Sturridge sent the former Arsenal man clean through on goal and he opened his Liverpool account with a measured finish before Alexander-Arnold’s deflected drive completed the rout.

“We wanted to show our best counter-pressing and a few of the goals came from that,” Klopp said. “We were also cool inside the penalty area” – cool, devastating and record-breaking.